Chapter SH, Problem 4.20EP

To determine

To find inverse of the function $f(x)=-3x+8$ .

Answer to Problem 4.20EP

  $f^{-1}(x)=\frac{8-X}{3}$

Explanation of Solution

Given information:

The function is $f(x)=-3x+8$ .

Calculation:

  $f(x)=-3x+8$

Replace $f(x)$with Y

  $Y=-3X+8$

Switch X with Y

  $X=-3Y+8$

Substract 8 from both sides

So,

  $X-8=-3Y$

Dividing both sides by -3

  $\frac{X-8}{-3}=\frac{-3Y}{-3}$

So,

  $\frac{X-8}{-3}=Y$

On simplification,

  $Y=\frac{8-X}{3}$

Then, the inverse function of $f(x)$is given below

  $f^{-1}(x)=\frac{8-X}{3}$