Q. 8 - Precalculus Enhanced with Graphing Utilities

Question

Find the inverse function of $f\left(x\right)= 3x-2$

Step-by-Step Solution

Answer

The inverse function is $y^{-1}=\frac{\left(x+2\right)}{3}$ 

Step 1. Given information

$y=3x-2$

To find the inverse of a function, we have to get the equation in terms of y

Step 2. Calculating the equation

$$\begin{gathered} y= 3x-2 \\ 3x=y+2 \\ x =\frac{\left(y+2\right)}{3} \end{gathered}$$

in terms of x,

$y^{-1 } = \frac{\left(x+2\right)}{3}$

here $y^{-1}$ is the inverse of the function