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

**Solution:**

Increasing functions are those functions that increase monotonically within a particular domain,

and decreasing functions are those which decrease monotonically within a particular domain.

Let x_{1} and x_{2} be any two numbers in R.

Then,

x_{1} < x_{2}

On multiplying both sides by 2, we get

⇒ 2x_{1} < 2x_{2}

Now, taking the base of e on both sides to meet the requirement of the given question.

⇒ e^{2x}1 < e^{2x}2

= f (x_{1}) < f (x_{2})

Thus, f is strictly increasing on R

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.2 Question 2

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

**Summary:**

Hence we have concluded that the function given by f (x) = e^{2x }is strictly increasing on R