A function is said to be increasing function on (a, b) if

x₁ < x₂ => f(x₁ ) ≤ f(x₂ ) for all x₁ , x₂ ∈ (a, b)

A function is said to be strictly increasing function on (a, b) if

x₁ < x₂ => f(x₁ ) < f(x₂ ) for all x₁ , x₂ ∈ (a, b)

Ex: Let there is a function f(x) = 2x + 3

Let x₁ , x₂ ∈ R and let x₁ < x₂

Now, x₁ < x₂  => 2x₁ < 2x₂

                   => 2x₁ + 3 < 2x₂ + 3

                   => f(x₁ ) < f(x₂ )

Thus, x₁ < x₂ => f(x₁ ) < f(x₂ ) x₁ , x₂ ∈ R

So, f(x) is strictly increasing function on R.