Question

I need to know the inverse of the function step by step to really understand it.

Answer 1

To determine the inverse of a function:

`y=\frac{\sqrt[]{2x-3}}{3}`

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

`\begin{gathered} y=\frac{\sqrt[]{2x-3}}{3} \\ 3y=\sqrt[]{2x-3} \\ \text{square both side of the equation} \\ (3y)^2=(\sqrt[]{2x-3)^2} \\ 9y^2=2x-3 \\ 9y^2+3=2x \\ \text{divide both side by 2} \\ (2x)/(2)=(9y^2+3)/(2) \\ x=(9y^2+3)/(2) \\ \text{Then replacing y with x} \\ y=(9x^2+3)/(2) \end{gathered}`

Therefore inverse function for y = f(x) , x = g(y) where x ≥ 0

`y=(9x^2+3)/(2),\text{ where x }\ge0`

Hence the correct answer is Option C