Question

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

$f\left(x\right)=x+17$

Short answer

The inverse of the given function is$f^{-1}x=x-17$.

Step-by-step solution

Step 1. Given and explanation.

We have $f\left(x\right)=x+17$.

We will first replace $f\left(x\right)$by $y$. We will then replace the variables by each other. Then we will solve for$y$ and will replace$y$by$f^{-1}x$to get the inverse.

Step 2. Replacing f(x) by y and then interchange the variable.

We have $f\left(x\right)=x+17$.

Replacing $f\left(x\right)$by $y$gives us $y=x+17$.

Interchanging the variables gives us,

$x=y+17$.

Step 3. Finding inverse.

We have $x=y+17$.

We need to solve for $y$. So, subtracting $17$from both sides,

$$\begin{gathered} x-\left(17\right)=y+17-\left(17\right) \\ y=x-17 \end{gathered}$$
Replacing$y$by$f^{-1}x$ gives us the inverse as$f^{-1}x=x-17$.