Mathematics

The key insight is that inverse functions swap inputs and outputs—if a point $(a, b)$ lies on $g$, then $(b, a)$ lies on $g^{-1}$. Since $P(4, -2)$ is on the original function's graph, you're simply reflecting that point across the line $y = x$ to find where it lands on the inverse function's graph.

The key insight is that inverse functions swap inputs and outputs—if a point $(a, b)$ lies on $g$, then $(b, a)$ lies on $g^{-1}$. Since $P(4, -2)$ is on the original function's graph, you're simply reflecting that point across the line $y = x$ to find where it lands on the inverse function's graph.