Question

What is the relation between f(x) and ℓ when the maximum value or greatest value function f is defined on a set A and ℓ ∈ f(A)?

(a) f(x) < &ell; ∀ x  ∈ A

(b) f(x) ≤ &ell; ∀ x  ∈ A

(c) f(x) = &ell; ∀ x  ∈ A

(d) f(x) > &ell; ∀ x  ∈ A

This question was posed to me in an online interview.

I'm obligated to ask this question of Derivatives Application topic in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Right answer is (b) f(x) ≤ &ell; ∀ x  ∈ A

For explanation: A function f defined on a set A and &ell; ∈ f(A), then &ell; is the maximum or the greatest value of f in A if f(x) ≤ &ell; ∀ x  ∈ A and the minimum or the least value of f in A if f(x) ≥ &ell; ∀ x ∈ A.