Question

Function f(x) = {(-1, when x < - 1), (-x, when - 1 ≤ x ≤ 1), (1, when x > 1) continuous -

(A) Only at x = 1

(B) Only at  x = - 1

(C) At both x = 1 and x = - 1

(D) Neither at x = 1 nor at x = - 1

Answer 1

Answer is (D) Neither at x = 1 nor at x = - 1

f(-1 - 0) = - 1, f(-1) = -(-1) = 1

⇒ f(-1 - 0) ≠ f(-1)

⇒ f(x) is not continuous at x = - 1

Further, f(1) = -1

f(1 + 0) = 1 ⇒ f(1) ≠ f(1 + 0)

⇒ f(x) is not continuous at x = 1.