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 x₁ and x₂ be any two numbers in R.

Then,

x₁ < x₂

On multiplying both sides by 2, we get

⇒ 2x₁ < 2x₂

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

⇒ e^2x1 < e^2x2

= f (x₁) < f (x₂)

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