If f(x) = √(x-3) has domain x ≥ 3 and range y ≥ 0, what is the domain of f^-1(x)?

The domain of an inverse function is the range of the original function, because inversion swaps inputs and outputs. The function $f(x)=\sqrt{x-3}$ outputs only non-negative values, so its range is $y\ge0$, and the domain of $f^{-1}$ is $x\ge0$, choice J. As a check, $f^{-1}(x)=x^2+3$ for $x\ge0$ (the restriction keeps it one-to-one). Choice F ($x\ge3$) is the domain of $f$ itself. Choice G ($x\le0$) has the inequality reversed. Choice H (all real numbers) would be true of the formula $x^2+3$ alone, but the inverse must be restricted so that it reverses $f$.