Question

Show that the function given by $f(x) = e^{2x}$ is strictly increasing on $R$.

Answer 1

Let $x_1$ and $x_2$ be any two numbers in $R$.
Then, we have:
$x_1<x_2=2x_1<2x_2=e^{2x_1}<e^{2x_2}=f(x_1)<f(x_2)$
Hence, f is strictly increasing on R.