Chapter 4, Problem 58SGR

To determine

To find the inverse of the function $f\left(x\right)=\frac{3x+4}{7}$ .

Answer to Problem 58SGR

  $f^{-1}\left(x\right)=\frac{1}{3}\left(7x-4\right)$

Explanation of Solution

Given:

  $f\left(x\right)=\frac{3x+4}{7}$

Calculation:

Let us consider,

  $y=\frac{3x+4}{7}$

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

  $\begin{array}{l}x=\frac{3y+4}{7}\\ \Rightarrow 7x=3y+4\\ \Rightarrow 3y=7x-4\\ \Rightarrow y=\frac{1}{3}\left(7x-4\right)\\ \therefore f^{-1}\left(x\right)=\frac{1}{3}\left(7x-4\right)\end{array}$