Mathematics

The key insight is recognizing what happens when you compose a function with its inverse: they "undo" each other. Since $g$ is the inverse of $f$, applying $f$ first and then $g$ simply returns you to where you started. You don't need to find the explicit formula for $g(x)$ — just use the definition that $g(f(x)) = x$ for all $x$ in the domain.

The key insight is recognizing what happens when you compose a function with its inverse: they "undo" each other. Since $g$ is the inverse of $f$, applying $f$ first and then $g$ simply returns you to where you started. You don't need to find the explicit formula for $g(x)$ — just use the definition that $g(f(x)) = x$ for all $x$ in the domain.