Suppose $f\left(x\right)={\left(x+1\right)}^2$ for $x\ge -1$.  If g(x) is the function whose graph is the reflection of the graph of f(x) with
respect to the line y = x, then g(x) equals 

$\mathrm{Given} \mathrm{that} f\left(x\right)={\left(x+1\right)}^2,x\ge -1.$

Now, if g(x) is the reflection of f(x) in the line y = x, then

g(x) is an inverse function of y = f(x).

$\begin{array}{l}\mathrm{Given} y={\left(x+1\right)}^2 \left(x\ge -1 \mathrm{and} y\ge 0\right)\\ \mathrm{or} x=\pm \sqrt{y}-1\\ \mathrm{or} g\left(x\right)=f^{-1}\left(x\right)=\sqrt{x}-1, x\ge 0\end{array}$