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.