Answer
$f(x)=\sqrt{3-x}$
$f^{-1}(x)=3-x^{2}$
Work Step by Step
$f(x)=\sqrt{3-x}$, for $x\le3$
Substitute $f(x)$ by $y$:
$y=\sqrt{3-x}$
Solve the equation for $x$. Start by squaring both sides:
$y^{2}=(\sqrt{3-x})^{2}$
$y^{2}=3-x$
Take $x$ to the left side and $y^{2}$ to the right side:
$x=3-y^{2}$
Interchange $x$ and $y$:
$y=3-x^{2}$
Substitute $y$ by $f^{-1}(x)$:
$f^{-1}(x)=3-x^{2}$
The graph of both the original function and its inverse is shown in the answer section.
