Question

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

Short answer

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

Step-by-step solution

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