Question

Use the definition of inverses to determine whether f and g are inverses.Xf(x)=2x-8, g(x) = 2 +4Are the f and g inverses of each other?OYesO №o***

Answer 1

For f and g to be inverses, then

`f(g(x))=g(f(x))=x`

Now

`\begin{gathered} f(g(x))=2((x)/(2)+4)-8 \\ =(2x)/(2)+8-8 \\ =x \end{gathered}`

Also

`\begin{gathered} g(f(x))=(2x-8)/(2)+4 \\ =(2x-8+8)/(2) \\ =(2x)/(2) \\ =x \end{gathered}`

Since we got x in both cases, hence f and g are inverses of each other

The answer is YES