Let f(x) = x 3 − x 2 + x + 1 and g(x) =, then:

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

g(x) is continuous & derivable at x = 1

g(x) is continuous but not derivable at x = 1

g(x) is neither continuous nor derivable at x = 1

g(x) is derivable but not continuous at x = 1

Text Solution

Verified by Experts

The correct answer is:

f(x) = x 3 − x 2 + x + 1

f '(x) = 3x 2 − 2x + 1 > 1 ,

f(x) is strictly increasing

So g(x) = =

g(1) = f(1) = 1 – 1 + 1 + 1 = 2 =

= 3 – 1 + 1 = 3

g(x) is neither continous nor differentiable at x = 1

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