Question

Given the function:f(x) = sqrt(3x + 6)What is the inverse function of f(x)?

Answer 1

Given the function:

`f(x)=\sqrt[]{3x+6}`

to find the inverse function, first we have to set f(x) = y, and the solve for y. In this case, we have the following:

`\begin{gathered} y=f(x) \\ \Rightarrow y=\sqrt[]{3x+6} \\ \Rightarrow y^2=3x+6 \\ \Rightarrow y^2-6=3x_{} \\ \Rightarrow(y^2-6)/(3)=x \end{gathered}`

therefore, the inverse function is:

`f^(-1)(x)=(x^2-6)/(3)`