Question

What is the inverse of f(x) = 1/2 x -5

Answer 1

We can calculate the inverse of a function y=f(x) by clearing x as x=g(y).

We have the function:

`f(x)=(1)/(2)x-5`

We can find the inverse as:

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

The inverse function is:

`f^(-1)(x)=2x+10`

Answer: f^-1(x)=2x+10