Question

For questions 3 and 4, find F -1(x), the inverse of F(x)

Answer 1

A function g(x) is the inverse funtion of f(x) if for y = f(x), x = g(y).

The given function is,

`f(x)=x-10`

where,

`y=f(x)`

Therefore,

`y=x-10`

Replace x with y

`x=y-10`

Solve for y by add 10 to both sides of the equation

`\begin{gathered} x+10=y-10+10 \\ x+10=y+0 \\ x+10=y \\ \therefore y=x+10 \end{gathered}`

Hence,

`\begin{gathered} f^(-1)(x)=g(x) \\ \therefore g(x)=x+10 \end{gathered}`

Therefore, the inverse of f(x) is x + 10.