Given
[tex]f(x)=x^2+4\text{ for x}\ge0[/tex]
The inverse is
[tex]\begin{gathered} f(x)=x^2+4 \\ replace\text{ f\lparen x\rparen with y} \\ y=x^2+4 \\ interchange\text{ x and y} \\ x=y^2+4 \\ solve\text{ for y} \\ y^2=x-4 \\ y=\sqrt{x-4} \\ f^{-1}(x)=\text{ }\sqrt{x-4} \end{gathered}[/tex]
[tex]\sqrt{x-4}[/tex]
Solution
