Answers
Answer:
[tex]f^{-1}(x)=\sqrt{x+1}-3[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=y=x^2+6x+8[/tex] with the domain restriction [tex]\{x\geq -3\}[/tex].
And we want to find the inverse of our function.
To find the inverse of our function, we take the following steps:
1) Swap x and y. 2) Solve for y.Therefore, our inverse will be:
[tex]x=y^2+6y+8[/tex]
First, let's subtract 8 from both sides. So:
[tex]x-8=y^2+6y[/tex]
To solve for y, we can complete the square. To complete the square, we:
1) Divide the coefficient of the b term by 2. 2) Square that. 3) Add that number to both sides.Our b term is 6. [tex]6/2=3[/tex], and [tex]3^2=9[/tex]. So, we will add 9 to both sides. This yields:
[tex](x-8)+9=(y^2+6y+9)[/tex]
Simplify the left. Complete the square on the right. So:
[tex]x+1=(y+3)^2[/tex]
Take the square root of both sides and solve for y:
[tex]y+3=\sqrt{x+1}\Rightarrow y=\sqrt{x+1}-3[/tex]
Subtract 3 from both sides. So, our inverse is:
[tex]f^{-1}(x)=\sqrt{x+1}-3[/tex]
Part 2)
See below for graph.
Here is also a good time to reinforce the idea of inverses. Notice that the domain of our original function f(x) is [tex]x\geq-3[/tex]. So, this means that the range of f(x) is (looking at the graph) is [tex]y\geq-1[/tex].
When we find the inverse, we will flip the domain and range. Therefore, the domain of our inverse function will be the range of our original function, and the range of our inverse function will be the domain of our original function.
From the graph, we can see that f⁻¹(x) has a domain of [tex]x\geq-1[/tex] and a range of [tex]y\geq -3[/tex]. Therefore, their domain and range are indeed opposites.
And we're done!
Related Questions
Slove this inequality
5+7x ≤ 26
Answers
Answer:
x<3
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
7x+5<26
Step 2: Subtract 5 from both sides.
7x+5−5<26−5
7x<21
Step 3: Divide both sides by 7.
7x/7<21/7
x<3
Answer:
3
Step-by-step explanation:
Subtract 5 from both sides.
7x<21
7 goes into 21, 3 times.
Therefore, x<3
If 5x = -35, then find the value of -28 + 4x
Answers
Answer:
x=-7
Step-by-step explanation:
-28-28=-56
hope it will help you!!!!
mark as brainiest
Please help me similar triangles
Answers
Answer:
30 degrees
Step-by-step explanation:
14 + 5 + 11 = 30
180 / 30 = 6
6 x 5 = 30
So:
The smaller triangle is 30 degrees.
Hope this helps!
What is 1.8 divided by 2? Show Work
Answers
Answer:
0.9
Step-by-step explanation:
Unless is there is another way to answer this question, all you have to do is put it into a calculator.
Write the equation of a line passing through the points (-2,0) and (7,9) in point-slope form.
Answers
Answer:
Y+0=1(x+2)
Step-by-step explanation:
Modern car company has come out with a new car model, Market analysts predict that 4,900 cars will be sold in the first month and that sales will drop by 100 cars per month after that during the first year. Write out the first five terms of the sequence, and find the number of sold cars predicted for the twelfth month. Find the total predicted number of sold cars for the first year. a. The first five terms of the sequence are (Use a comma to separate answers.)
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Number of cars sold in first month = 4900
Sales drop by 100 cars per month for the first year:
A(x) = a - 100(x - 1)
No = sale In first month = 4900
First five months
Ist month :
a = 4900
2nd :
4900 - 100 = 4800
3rd :
4800 - 100 = 4700
4th:
4700 - 100 = 4600
5th:
4600 - 100 = 4500
First five terms : (4900,4800,4700,4600, 4500)
Predicted sales for 12th month :
A(12) = 4900 - 100(12 - 1)
A(12) = 4900 - 1100
= 3800
Total sales for the first year:
4900+4800+4700+4600+4500+4400+4300+4200+4100+4000+3900+3800) =
= 52,200
I need help with this question
Answers
Answer:
4.20
Step-by-step explanation:
Answer:
4.2
Step-by-step explanation:
it starts with 2.80 and four is that dou led so we have to find half of 2.8 then add it to find three (I'm bad at explaining)
classify each equation below as a formula , a literal equation ,or both.
c=2d , a=1/2bh , y=2x-1, p=2e+ 2w
Answers
delete my answer please its useless
A swimmer competes in a 200 meter free style race. If the swimmer finishes the race in 5 minutes. How fast was the swimmer swimming?
Answers
Answer:
40meters per minutes
Step-by-step explanation:
Answer:
40m/min
Step-by-step explanation:
200m/5min
40m/min
Hope this helps!
The program recommends a constant intensity for 3 visits, increasing intensity over 3 visits, and then decreasing intensity for 3 visits before restarting the pattern. Which sets of values could be the intensities of Amber's exercise during the fourth, fifth, and sixth visits?
Answers
Answer and Step-by-step explanation:
Solution:
Set of values that are intensities of Ambers exercise during fourth, fifth and sixth visits:
63%, 63%,63%, 66%, 69%, 72%, 66%, 62%, 58%, 67%, 67%, 67%, 63%, 65%, 67%, 67%, 72%, 77%/
Program recommends a constant intensity for 3 visits,
Increasing intensity over 3 visits,
And decreasing intensity for 3 visits,
Set of values, which are intensities of Ambers exercise during fourth visits:
66%.
69%,
72%,
Set of values, which are intensities of Ambers exercise during fifth visits:
63%,
65%,
67%,
Set of values, which are intensities of Ambers exercise during sixth visits:
67%,
72%,
77%,
Its decreasing.
2(x + 9) = 4(x - 7) + 2
Answers
Answer:
x = 22
Step-by-step explanation:
Step 1: Write equation
2(x + 9) = 4(x - 7) + 2
Step 2: Solve for x
Distribute: 2x + 18 = 4x - 28 + 2Combine like terms: 2x + 18 = 4x - 26Subtract 2x on both sides: 18 = 2x - 26Add 26 to both sides: 44 = 2xDivide both sides by 2: 22 = xRewrite: x = 22Step 3: Check
Plug in x to verify it's a solution.
2(22 + 9) = 4(22 - 7) + 2
2(31) = 4(15) + 2
62 = 60 + 2
62 = 62
Answer:
x=22
Step-by-step explanation:
2x+18=4x-28+2
2x+12=4x-26
2x+44=4x
44=2x
22=x
Use the fact that 521•73=38,033 Enter the exact product of 521•73
Answers
Answer:
38,033
Step-by-step explanation:
Your homework grades are 92, 87, 74, 96, 83, 88, 91, 82, and 85. What score on your next homework will make the median and the mode equal? List the scores in order from least to greatest. You can use the strategy Systematic Guess and Check to help you find the solution.
Answers
Answer:Next homework Score should be 87.
Step-by-step explanation:
STEP 1
Listing the scores in ascending order ie from least to greatest gives
74, 82, 83, 85, 87, 88, 91,92, 96
STEP 2
we find the median--- The median score is the score that is in the middle of the set of results when arranged from lowest to highest as we have done above , which give us 87 as the median.
74, 82, 83, 85, 87, 88, 91,92, 96
Also Mode is the score with the highest frequency , ie the score which appears more than other numbers. For now we have no mode as all the numbers occurred once
Therefore in next exam, I should get a score of 87, making my scores to become
74, 82, 83, 85, 87, 87, 88, 91,92, 96
Now my mode becomes 87 ( highest frequency of occurrence ) and
My median becomes (87+ 87)/2 = 87 ( with the addition of a new score the total score become ten, which is now even, so we divide the addtion of the two middle numbers by 2 )
Ammy wrote 66 as an expression equivalent to (62)4 . Her math partner writes 68. Who is correct? Why?
Answers
Answer:
Ammy is correct
Step-by-step explanation:
Ammy's math partner is correct.
Applying the "power of power rule" of exponents, if we have numbers raised by another number, what is needed to be done is to simply multiply the powers.
Thus: [tex] (x^a)^b) = x^{a*b} = x^{ab} [/tex]
Applying this rule, the equivalent expression to [tex] (6^2)^4 = 6^{2*4} = 6^8 [/tex].
Therefore, Ammy's math partner is correct, while Ammy is wrong.
In a 30 pack of Skittles, 30% are red. How many Skittles are red?
Answers
Answer: 9 skittles are red
Answer:
9
Step-by-step explanation:
30/100×30
=3/10×30
=3/1×3
=9
6.04x10 minus 3 cubed
Answers
Answer: .00604
Step-by-step explanation:
Hope this helps
Simplify the following expression to simplest form using only positive exponents.
(32x^-15y^25)^-2/5
Answers
Answer:
[tex]\frac{x^{6} }{4y^{10} }[/tex]
Step-by-step explanation:
THIS is the answer if the equation looks like this. [tex](32x^{-15} y^{25} )^{-2.5}[/tex]
HELP ME PLZZI NEED HELP WITH THIS!!
Answers
Answer:
The answer is C
Step-by-step explanation:
You would move the dot on the number to the right 5 spots, ending up at -4.
which two features are part of a line graph
Answers
Answer:
Your answer is: 1) y-axis (vertical) 2) x-axis (horizontal)
Step-by-step explanation:
Hope this helped : )
Your local radio station is having their yearly music player and concert ticket giveaway For one minute every fifth called her will win a new player in every step of the college will win concert tickets you were just the first quality win both in music player in concert tickets what number was I ?
Answers
Complete Question:
Your local radio station is having their yearly music player and concert ticket giveaway For one minute every fifth called will win a new player and every seventh caller will win concert tickets you were just the first quality win both in music player in concert tickets what number were you ?
Answer:
The 35th person
Step-by-step explanation:
Given
[tex]New\ Player = 5th[/tex]
[tex]Concert\ Ticket = 7th[/tex]
Required
Determine your position
To do this, we simply need to take LCM of the given parameters;
[tex]5 = 1 * 5[/tex]
[tex]7 = 1 * 7[/tex]
The LCM is as follows:
[tex]LCM = 1 * 5 * 7[/tex]
[tex]LCM = 35[/tex]
Hence:
You're the 35th person
Someone help please!!
Answers
Answer:
B
Step-by-step explanation:
Even though -3.613 has more digits, if you add a zero to -3.63 it becomes -3.630. -3.630 is greater than -3.613.
Answer:
b i think
Step-by-step explanation:
Can someone help with this one?
Answers
Answer:
3!
Step-by-step explanation:
Kiana wants to purchase a new bicycle for $ 225.45 and helmet for $12.55. If the sales tax rate is 7%, what will be the total amount of Kiana’s purchase including sales tax? 7.13A
Answers
Answer:
$254.66
Step-by-step explanation:
225.45 + 12.55 = 238
7% of 238 = 0.07 × 238 = 16.66
16.66 + 238 = 254.66
1 2/2 dived by - 1/5
Answers
Answer:
-10
Step-by-step explanation:
1 2/2= 2
2/(-1/5)=(-10)
Answer:
-10
Step-by-step explanation:
1 2/2 / -1/5
2 × 5 / -1/5 × 5
10 / - 1
10 × -1 / -1 × -1
-10 / 1
-10
Monsieur Anatole est un artisan spécialiser dans la fabrication de colliers. Il dispose 3 717 perles rouges et de 2 205 perles blanches. En utilisant toutes ses perles, il réalise au maximum de colliers identique. La réalisation de chaque collier lui coute 9,84 €. Un deuxième artisan, Monsieur Bernards, utilise la totalité de ces 1472 perles rouges et 2 898 perles blanches pour fabriquer un maximum de colliers identiques. La fabrication d'un collier lui revient à 8,48 €. Les deux artisans décident de fixer le prix de vente de chaque colliers selon la constitution, à savoir : 22 centimes d'euro par perle rouge et 13 centimes par perles blanches. Sur la vente d'un collier, quel artisan réalise le meilleure bénéfice ?
Answers
Answer:
Sur la vente d'un collier, l'artisan qui a fait le meilleur profit était Monsieur Bernard
Step-by-step explanation:
a) Pour Monsieur Anatole
Nous trouvons le plus grand diviseur commun de 3717 et 2205
Par conséquent, le plus grand diviseur commun = 63
Le nombre de colliers qu'il a fabriqués = 63
Découvrir combien de perles rouges et blanches il a utilisées
Pour les perles rouges =
= 3717/63 = 59 perles
Pour les perles blanches
= 2205/63 = 35 perles blanches
il fabrique 63 colliers avec 59 perles rouges et 35 perles blanches
On nous dit dans la question que:
Les deux artisans décident de fixer le prix de vente de chaque collier selon la constitution, à savoir: 22 centimes d'euro par perle rouge et 13 centimes par perle blanche.
Le prix de vente du collier =
0,22 × 59 + 0,13 × 35 = 17,53 €
Prix de revient = 9,84 €
Le profit est calculé comme suit:
17,53 € - 9,84 € = 7,69 €
Nous calculons le pourcentage de profit
= Bénéfice / Prix de revient × 100
= 7,69 / 9,84 × 100
= 78,150406504%
= 78,2%
b) Pour Monsieur Bernard
Le GCD de 1472 et 2898 = 46
Par conséquent, il a fait 46 colliers
Le nombre de perles rouges = 1472/46
= 32 perles rouges
Le nombre de perles blanches = 2898/46
= 63 perles blanches
Les deux artisans décident de fixer le prix de vente de chaque collier selon la constitution, à savoir: 22 centimes d'euro par perle rouge et 13 centimes par perle blanche.
Le prix de vente de chaque colliers = 32 × 0,22 + 63 × 0,13 = 15,23 €
Le coût Prix du collier = 8,48 € chacun
Le profit qu'il a réalisé = 15,23 € - 8,48 €
= 6,75 €
Nous calculons le pourcentage de profit
= Bénéfice / Prix de revient × 100
= 6,75 / 8,48 × 100
= 79,5990566%
= 79,6%
Sur la vente d'un collier, l'artisan qui a fait le meilleur profit était Monsieur Bernard
Which expression does the graphic represent?
○ 7-1
○ 7-(-1)
○ 8-1
○ 8-(-1)
Answers
8-1
if two is he same as to and too how are they different
Answers
Answer:
two is a number
too means in addition
to means motion in the direction
Step-by-step explanation:
To raise a product to a power raise each factor to the power and multiply the results. Is it true or false?
Answers
Answer:
True
Step-by-step explanation:
Hope this helps x
True
Consider two numbers a and b
Their product will be [tex]\sf a \times b = (ab) [/tex]
Suppose I want to raise this product to a power, say m
That is, [tex]\sf (ab)^m [/tex]
By rules of indices,
[tex]\sf (ab)^m = a^m \times b^m [/tex]
So, we have to raise the individual factors of the product to the power and multiply the results.
Hence the given statement is true.
An arithmetic series contains 14 numbers. The first number is 12. The last number is 38. What is the sum of the series?
A. 312
B. 350
C. 494
D. 700
Answers
Answer:
B. 350
Step-by-step explanation:
done on edge
The sum of the sequence is 350 if the arithmetic series contains 14 numbers. The first number is 12. The last number is 38 option (B) is correct.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
It is given that:
An arithmetic series contains 14 numbers.
The first number is 12.
The last number is 38.
As we know, the sum of the arithmetic sequence or series is given by:
S = (n/2)(a + l)
Here, S is the sum of the AP
n is the number of terms
a is the first term
l is the last term
n = 14
a = 12
l = 38
S = (14/2)(12 + 38)
S = (7)(50)
S = 350
Thus, the sum of the sequence is 350 if the arithmetic series contains 14 numbers. The first number is 12. The last number is 38 option (B) is correct.
Learn more about the sequence here:
brainly.com/question/21961097
#SPJ5
Which expression has the same value as 59.2 - 84.7? *
27 points
A. 84.7 - 59.2
B. -84.7 + (-59.2)
C. 59.2 - (-84.7)
D. 59.2 + (-84.7)
Answers
Answer:
D. 59.2 + (-84.7)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO