Chapter 4, Problem 20PT

To determine

To find the inverse of the function $f\left(x\right)=\frac{3}{4}x+12$ .

Answer to Problem 20PT

  $f^{-1}\left(x\right)=\frac{4}{3}x-16$

Explanation of Solution

Given:

  $f\left(x\right)=\frac{3}{4}x+12$

Calculation:

Let us consider,

  $y=\frac{3}{4}x+12$

To find inverse function, replace $y$ by $x$ and then solve for $y$ in terms of $x$ . That is,

  $\begin{array}{l}x=\frac{3}{4}y+12\\ \Rightarrow \frac{3}{4}y=x-12\\ \Rightarrow y=\frac{4}{3}\left(x-12\right)\\ \Rightarrow y=\frac{4}{3}x-16\\ \therefore f^{-1}\left(x\right)=\frac{4}{3}x-16\end{array}$