Question

If the domain of the function F is restricted the X is greater or equal to zero what function is the inverse of F

Answer 1

The function is given as

`f(x)=9x^2-12,x\ge0`

To find the inverse of f(x)

Let f(x) = y

This implies

`y=9x^2-12`

Make x the subject of the equation

First, add 12 to both sides of the equation

`y+12=9x^2-12+12`

This gives

`y+12=9x^2`

Divide both sides of the equation by 9

`(y+12)/(9)=x^2`

Next, take the square root of both sides of the equation

`\begin{gathered} \sqrt[]{(y+12)/(9)}=\sqrt[]{x^2} \\ \Rightarrow x=\sqrt[]{(y+12)/(9)} \end{gathered}`

Let the inverse be g(x)

Hence, for the inverse substitute x for y

This gives

`g(x)=\sqrt[]{(x+12)/(9)}`