Question

Function to inverse function f(x) =2x/3-17

Answer 1

Answer:

Inverse function is $f^{-1}(x)=\frac{3}{2}x+\frac{51}{2}$.

Step-by-step explanation:

Given function is $f\left(x\right)=\frac{2}{3}x-17$.

Now we need to find the inverse of the given function.

Step 1: replace f(x) with y

$y=\frac{2}{3}x-17$

Step 2: switch x and y

$x=\frac{2}{3}y-17$

Step 3: solve for y

$x=\frac{2}{3}y-17$

$x+17=\frac{2}{3}y$

$\frac{3}{2}(x+17)=y$

$\frac{3}{2}x+\frac{51}{2}=y$

Hence required inverse function is $f^{-1}(x)=\frac{3}{2}x+\frac{51}{2}$.