10.1 inverses of simple quadratic and cubic functions

Answers

Answer 1

The inverse function of the cubic function is its opposite

The inverse function of [tex]f(x) = 5x^3[/tex] is [tex]f^{-1}(x) = \sqrt[3]{\frac x5}[/tex]

How to determine the inverse of the function?

The cubic function is given as:

[tex]f(x) = 5x^3[/tex]

Express f(x) as y

[tex]y = 5x^3[/tex]

Swap the positions of x and y

[tex]x = 5y^3[/tex]

Divide both sides by 5

[tex]y^3 = \frac x5[/tex]

Take the cube roots of both  sides

[tex]y = \sqrt[3]{\frac x5}[/tex]

Express y as an inverse function

[tex]f^{-1}(x) = \sqrt[3]{\frac x5}[/tex]

Hence, the inverse function of [tex]f(x) = 5x^3[/tex] is [tex]f^{-1}(x) = \sqrt[3]{\frac x5}[/tex]

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Related Questions

It refers to any software that is installed on a computer’s hard drive.

Answers

Answer:

Application Softwares

What is the first step in the talk method of conflict resolution?

Answers

Answer:

Communication is the first step.

Explanation:

Find the output, bbb, when the input, aaa, is 666. b = -1-7ab=−1−7a

Answers

The output of the given algebra b = -1 - 7a with the given input of a = 6 is calculated to be; b = -43

How to solve basic algebra?

We are given the algebra;

b = -1 - 7a

where;

a is the input

b is the output

Now, we are given the value of the input to be a = 6

Thus, output is calculated as;

b = -1 - 7(6)

b = -1 - 42

b = -43

Thus, the output of the given algebra with the given input is -43.

Read more about algebra at; https://brainly.com/question/723406

Answer:the answer is B

Explanation:

how far is the west side from the east side

Answers

Answer:

The distance between the East Coast and the West Coast of the United States ranges between 2,600 and 3,200 miles, depending on the route.

Explanation:

How far is West Coast to East Coast?

2,092 miles is the shortest distance from the East Coast to the West Coast. It would take you about a week or so to get there at 60 miles an hour.

What’s the distance between the east coast and West Coast?

The distance between the East Coast and the West Coast of the United States ranges between 2,600 and 3,200 miles, depending on the route.

Answer:

3,527 miles

Explanation:

The longest route covers approximately 3,527 miles and is referred to as Route 50

hope this helps

What are some helpful tips for performing well on the SAT?

Answers

Remove three incorrect answers from the equation. Always be aware of your errors. Pay attention to the connotation and context of what you're saying. Use Make the most of the evidence questions. Read passages in a strategic manner. Passage Introductions Should Not Be Ignored. Become engrossed in the passages. Before taking the test, read the section instructions. First, answer the questions you already know the answers to. Remove any wrong responses. Maintain a tidy appearance. Keep an eye out for stray marks. The majority of the time, your initial response is correct. There is just one response that is correct.

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