Question

The function f(x) = 5x+3 is one to one. Find an equation for f-1(x) the inverse function.

Answer 1

Given the function:

`f\mleft(x\mright)=5x+3`

To find the inverse function, we make x the subject of the equation.

`\begin{gathered} 5x=f(x)-3 \\ x=(f(x)-3)/(5) \end{gathered}`

Next, we replace x with f-1(x) and f(x) with x.

Therefore, the inverse function is:

`f^(-1)(x)=(x-3)/(5)`