Verify Functions Are Inverses Practice Test

$f(g(x))=\sqrt{x^2}=|x|$ and $g(f(x))=(\sqrt{x})^2=x$, so they are inverses for all real $x$ without restriction.

$f(g(x))=(\sqrt{x})^2=x$ but $g(f(x))=\sqrt{x^2}=-x$, so they are not inverses.

$f(g(x))=x^2$ and $g(f(x))=\sqrt{x}$, so they are inverses because the outputs match the original functions.

$f(g(x))=(\sqrt{x})^2=x$ (for $x\ge 0$) and $g(f(x))=\sqrt{x^2}=x$ (for $x\ge 0$), so they are inverses on the restricted domain.