Question

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

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

Short answer

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

Step-by-step solution

Step 1. Given

A function is given as$f\left(x\right)=\frac{1}{x+5}$

Step 2. Calculation

Let ,

$y=f\left(x\right)=\frac{1}{x+5}$

Now find the value of $x$in terms of $y$,

$$\begin{gathered} y=\frac{1}{x+5} \\ x+5=\frac{1}{y} \\ x=\frac{1}{y}-5 \end{gathered}$$

Therefore the inverse isrole="math" localid="1644990891266" $f^{-1}\left(x\right)=\frac{1}{x}-5$