Question

Determine whether the functions $f\left(x\right)=x-2$and$f\left(x\right)=x-2$ are inverse functions. (Lesson 7-8)

Short answer

$f\left(x\right)=x-2$and $g\left(x\right)=2x$are not inverse functions.

Step-by-step solution

Step 1. Given

The given functions are $f\left(x\right)=x-2$and $g\left(x\right)=2x$.

Step 2.To determine

We have to find whether the functions $\backslash \left[f\right(x)=x-2\backslash ]and\backslash \left[g\right(x)=2x\backslash ]$are inverse

functions.

Step 3.Calculation

For inverse functions we must have: $f\left(g\left(x\right)\right)=x$and $g\left(f\left(x\right)\right)=x$.

$\begin{array}{l}f\left(g\left(x\right)\right)\\ =f\left(2x\right)\\ =2x-2\ne x\end{array}$

It means$f\left(x\right)=x-2$ and $g\left(x\right)=2x$are not inverse functions.