Question

Determine whether each pair of functions are inverses of each other. Show your work.

Answer 1

We need to determine whether the functions below are inverses of each other:

`\begin{gathered} f(x)=(1)/(2)x-10 \\ \\ g(x)=2x+5 \end{gathered}`

When two functions F and G are inverses of each other, they satisfy the following result:

`F(G(x))=G(F(x))=x`

So, let's check whether the given functions are inverses of each other:

`\begin{gathered} f(g(x))=(1)/(2)g(x)-10 \\ \\ f(g(x))=(1)/(2)(2x+5)-10 \\ \\ f(g(x))=(2x)/(2)+(5)/(2)-10 \\ \\ f(g(x))=x-(15)/(2) \\ \\ \Rightarrow f(g(x))\\e x \end{gathered}`

Therefore, the given functions are not inverses of each other.