I have $f(x) = \sqrt x$, which means $f^{-1}(x) = x^2$.
I need to determine if the points $(a, f(a))$ where $a \geq 0$ lies on the graph of $f$ or $f^{-1}$. This was easier with points like $(2,4)$ or $(5, \sqrt 5)$ where I could easily plug in the numbers and solve the equation. Does the same hold where I just use the terms $a$ and $f(a)$ to solve the problem?