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Q.
Suppose $f(x) = (x + 1)^2$ for $x \geq - 1$. If $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x) =$
Given, $f(x)=(x+1)^{2}, x \geq-1$
and $g(x)$ is reflection of graph $f(x)$ in the line $Y=x$,
then $g(x)$ is the inverse of $f(x)$.
Let $y=(x+1)^{2}$
$\Rightarrow \sqrt{Y}=x+1$ (taking square root)
$\Rightarrow x=\sqrt{y}-1$
i.e., $f^{-1}(y)=\sqrt{y}-1$
or $g(x)=\sqrt{x}-1$