Example  QF.INV.3:  Suppose for $x\ge 0$, $f(x) = Ax^2 +k$. Verify that $g(x) =\sqrt{\frac {x-k} A}$ is the inverse function for $f$.
The algebra here is quite straight forward.
We check visually with mapping diagrams and graphs for.$f\circ g$  and  $g \circ f$.
Select the point x in the mapping diagram to move the point by mouse or use the scroll up or down key  to move by increments.
Mapping Diagram and Graph of $f\circ g$

Mapping Diagram and Graph of $g \circ f$