Question

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

$f\left(x\right)=x-12$.

Short answer

The inverse for the given function is$f^{-1}x=x+12$.

Step-by-step solution

Step 1. Given and explanation.

We have $f\left(x\right)=x-12$.

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$y$with$f^{-1}x$to get the inverse.

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

We have $f\left(x\right)=x-12$.

Replacing $f\left(x\right)$gives us $y=x-12$.

Interchanging the variables give us,

$x=y-12$

Step 3. Finding inverse.

We have $x=y-12$.

We need to solve for $y$. So, adding $12$both sides,

$$\begin{gathered} x+\left(12\right)=y-12+\left(12\right) \\ y=x+12 \end{gathered}$$
Replacing $y$by $f^{-1}x$gives usthe inverse as localid="1644937519769" $f^{-1}x=x+12$.