Question

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

Answer 1

Let x1 and x2 be any two numbers in R.
Then, we have:
x1<x2 $⇒$ 2x1<2x2 $⇒$ e2x1<e2x2 $⇒$ f(x1)<f(x2)

Hence, f is strictly increasing on R.