the function f(x)=-4x+9 has a range given by {1, -3, -7, -15, -19, -23} select the domain values of the function from the list. complete the explanation for how you arrived at your answer. btw this isn’t actually a test it’s assigned as hw but please help

Let's see what to do buddy....

_________________________________

Remember from now on ,

rang = output

and also Remember ,

output = y = f(x)

So : range = f(x)

So we must put the range number instead of f(x) and solve for x.

Let's do it...

=======================================

[tex]f(x) = 1[/tex]

[tex] - 4x + 9 = 1[/tex]

Both sides minus 9

[tex] - 4x = 1 - 9[/tex]

[tex] - 4x = - 8[/tex]

Negatives simplified

[tex]4x = 8[/tex]

Divided both sides by 4

[tex]x = \frac{8}{4} \\ [/tex]

[tex]x = 2[/tex]

_________________________________

[tex]f(x) = - 3[/tex]

[tex] - 4x + 9 = - 3[/tex]

[tex] - 4x = - 3 - 9[/tex]

[tex] - 4x = - 12[/tex]

[tex]4x = 12[/tex]

[tex]x = \frac{12}{4} \\ [/tex]

[tex]x = 3[/tex]

_________________________________

[tex]f(x) = - 7[/tex]

[tex] - 4x + 9 = - 7[/tex]

[tex] - 4x = - 7 - 9[/tex]

[tex] - 4x = - 16[/tex]

[tex]4x = 16[/tex]

[tex]x = \frac{16}{4} \\ [/tex]

[tex]x = 4[/tex]

_________________________________

[tex]f(x) = - 15[/tex]

[tex] - 4x + 9 = - 15[/tex]

[tex] - 4x = - 15 - 9[/tex]

[tex] - 4x = - 24[/tex]

[tex]4x = 24[/tex]

[tex]x = \frac{24}{4} \\ [/tex]

[tex]x = 6[/tex]

_________________________________

[tex]f(x) = - 19[/tex]

[tex] - 4x + 9 = - 19[/tex]

[tex] - 4x = - 19 - 9[/tex]

[tex] - 4x = - 28[/tex]

[tex]4x = 28[/tex]

[tex]x = \frac{28}{4} \\ [/tex]

[tex]x = 7[/tex]

_________________________________

[tex]f(x) = - 23[/tex]

[tex] - 4x + 9 = - 23[/tex]

[tex] - 4x = - 23 - 9[/tex]

[tex] - 4x = - 32[/tex]

[tex]4x = 32[/tex]

[tex]x = \frac{32}{4} \\ [/tex]

[tex]x = 8[/tex]

=======================================

So the domain values are :

x = { 2 , 3 , 4 , 6 , 7 , 8 }

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

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