Question

In the following exercises, find the inverse of each function.

$f\left(x\right)=6x-11$

Short answer

The inverse is$f^{-1}\left(x\right)=\frac{y+11}{6}$

Step-by-step solution

Step 1. Given

A function is given as$f\left(x\right)=6x-11$

Step 2. Calculation

Let $y=f\left(x\right)$,

$y=6x-11$

Find the value of $x$in terms of $y$,

$$\begin{gathered} y=6x-11 \\ 6x=y+11 \\ x=\frac{y+11}{6} \end{gathered}$$

Therefore the inverse is$f^{-1}\left(x\right)=\frac{y+11}{6}$