Question

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

Answer 1

The given function is f( x )= e 2x , strictly increasing on R.

Let x 1 and x 2 be any two numbers in R.

If x 2 > x 1 ; then,

2 x 2 >2 x 1 e 2 x 2 > e 2 x 1 f( x 2 )>f( x 1 )

Thus, f( x ) is strictly increasing on R.