Question

Find the inverse of the function

$f\left(x\right)=5x-3$

Short answer

The inverse of $f\left(x\right)=5x-3$is

$f^{-1}\left(x\right)=\frac{x+3}{5}$

Step-by-step solution

Given information

Given the function$f\left(x\right)=5x-3$

Replace f(x) with y and then x,y

Replacing, we get

$$\begin{gathered} f\left(x\right)=5x-3 \\ y=5x-3 \\ x=5y-3 \\ x+3=5y \\ y=\frac{x+3}{5} \end{gathered}$$

Substitute f-1(x) for y

Substituting, we get

$f^{-1}\left(x\right)=\frac{x+3}{5}$

Verify f(f-1(x))=x

Substituting the values, we get

$$\begin{gathered} f\left(\frac{x+3}{5}\right)=5\left(\frac{x+3}{5}\right)-3 \\ f\left(\frac{x+3}{5}\right)=x+3-3 \\ f\left(\frac{x+3}{5}\right)=x \end{gathered}$$

So the functions are inverses