The function is given as
[tex]f(x)=9x^2-12,x\ge0[/tex]
To find the inverse of f(x)
Let f(x) = y
This implies
[tex]y=9x^2-12[/tex]
Make x the subject of the equation
First, add 12 to both sides of the equation
[tex]y+12=9x^2-12+12[/tex]
This gives
[tex]y+12=9x^2[/tex]
Divide both sides of the equation by 9
[tex]\frac{y+12}{9}=x^2[/tex]
Next, take the square root of both sides of the equation
[tex]\begin{gathered} \sqrt[]{\frac{y+12}{9}}=\sqrt[]{x^2} \\ \Rightarrow x=\sqrt[]{\frac{y+12}{9}} \end{gathered}[/tex]
Let the inverse be g(x)
Hence, for the inverse substitute x for y
This gives
[tex]g(x)=\sqrt[]{\frac{x+12}{9}}[/tex]
