Question

What is the mathematical expression for a function to be strictly increasing on (a,b)?

(a) x1 < x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)

(b) x1 < x2 ⇒ f(x1) ≥ f(x2) ∀ x1, x2 ∈ (a,b)

(c) x1 = x2 ⇒ f(x1) ≤ f(x2) ∀ x1, x2 ∈ (a,b)

(d) x1 = x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)

I have been asked this question during an online exam.

I'd like to ask this question from Derivatives Application in division Application of Derivatives of Mathematics – Class 12

Answer 1

Right choice is (a) x1 < x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b)

The best explanation: A function f : (a,b) → R is said to be strictly increasing on (a,b) if x1< x2 ⇒ f(x1) < f(x2) ∀ x1, x2 ∈ (a,b). (a,b) may be replaced by [a,b] or any interval in the definition.