Question

Find the inverse of the function ,$f\left(x\right)=8x+5$

Short answer

The inverse of $f\left(x\right)=8x+5$is

$f^{-1}\left(x\right)=\frac{x-5}{8}$

Step-by-step solution

Given information

Given the function$f\left(x\right)=8x+5$

Replace f(x) with yand then x,y

Replacing, we get

$$\begin{gathered} f\left(x\right)=8x+5 \\ y=8x+5 \\ x=8y+5 \\ x-5=8y \\ \frac{x-5}{8}=y \end{gathered}$$

Substitutef-1(x) for y

Substituting , we get

$f^{-1}\left(x\right)=\frac{x-5}{8}$

Verify f(f-1(x))=x

Substituting the values, we get

$$\begin{gathered} f\left(\frac{x-5}{8}\right)=8\left(\frac{x-5}{8}\right)+5 \\ f\left(\frac{x-5}{8}\right)=x-5+5 \\ f\left(\frac{x-5}{8}\right)=x \end{gathered}$$

So the functions are inverses