Question

If f(x) = {(x, 0 ≤ x ≤ 1), (2x - 1, 1 < x), then

(A) f is discontinuous at x = 1

(B) f is differentiable at x = 1

(C) f is continuous but not differentiable at x = 1

(D) None of these

Answer 1

Answer is (C) f is continuous but not differentiable at x = 1

Hence, function is continuous at x = 1

Therefore, Lf′(1) ≠ Rf′(1)

Hence, function is not differentiable at x = 1.