Functions, graphs and inverses practice question 10

In $f\bigl(g(x)\bigr)$, $g$ acts first and $f$ acts on its output. Starting from $e^{2x}$, which operations turn it into $h(x)$?

Cover up $e^{2x}$ in the formula for $h$ and call what is under your hand $v$. Whatever is left is $f(v)$.

Check your candidate by substituting $v = e^{2x}$ back in: you must recover exactly $\sqrt{1 + e^{2x}}$.