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PoeticAesthetics

Define

f(x) and y are two different ways of denoting the same thing. Thus...

f(x) = 9x - 8 is the same as y = 9x - 8

Inverse: the inverse of a function is the resulting equation when x and y switch places and the equation is solved for x

Solve

Switch the places of x and y in the given equation:

y = 9x - 8 ---> x = 9y - 8

Solve the new equation for y (isolate y on the left side of the equation)

x = 9y - 8

x + 8 = 9y - 8 + 8

x + 8 = 9y

(x + 8) / 9 = 9y / 9

(x + 8)/9 = y

y = (x + 8) / 9

y = [tex]\frac{x+8}{9}[/tex]

Now you have the inverse of f(x) = 9x - 8:

A) [tex]f^{-1}[/tex] =[tex]\frac{x + 8}{9}[/tex]

Key Terms

inverse

Answer:

A. [tex]f^{-1}(x)=\frac{x+8}{9}[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=9x-8[/tex]. We are asked to find the inverse function for our given function.

First of all, we will rewrite [tex]f(x)[/tex] as [tex]y[/tex] as:

[tex]y=9x-8[/tex]

To find the inverse function, we will interchange x and y variables and then solve for y.

[tex]x=9y-8[/tex]

Now, we will add 8 on both sides of our given equation.

[tex]x+8=9y-8+8[/tex]

[tex]x+8=9y[/tex]

Switch sides:

[tex]9y=x+8[/tex]

Now, we will divide both sides of our equation by 9.

[tex]\frac{9y}{9}=\frac{x+8}{9}[/tex]

[tex]y=\frac{x+8}{9}[/tex]

Now, we will replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex] as:

[tex]f^{-1}(x)=\frac{x+8}{9}[/tex]

Therefore, the inverse function for our given function would be [tex]f^{-1}(x)=\frac{x+8}{9}[/tex] and option A is the correct choice.

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