Question

Find the inverse of the following: f(x) = (4x +5)^(1/2)

Answer 1

To find the inverse, we are going to replace f(x) by y as:

`y=√(4x+5)`

Then, we need to solve for x as:

`\begin{gathered} y^2=4x+5 \\ y^2-5=4x \\ (y^2-5)/(4)=x \\ x=(y^2-5)/(4) \end{gathered}`

Finally, we need to interchange y and x as:

`y=(x^2-5)/(4)`

Answer: the inverse of the function is:

`y=f^(-1)(x)=(x^2-5)/(4)`