Let's start finding the inverse of the function by changing f(x) to y:
[tex]y=x^2+2[/tex]
We then interchange x and y, getting:
[tex]x=y^2+2[/tex]
We now solve for y.
[tex]\begin{gathered} y^2=x-2 \\ y=\sqrt[]{x-2} \end{gathered}[/tex]
Hence, the inverse of the function f(x) = x^2 + 2 is:
[tex]f^{-1}(x)=\pm\sqrt[]{x-2}[/tex]
Since we are only considering the domain x >= 0, we will only consider the inverse of the function that is positive, that is:
[tex]f^{-1}(x)=\sqrt[]{x-2}[/tex]
The plot of the function and its inverse is shown in the figure above.
