Let f : R → R be any function and g (x) = . Then g is

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

Published by: CGP EDU Academic Team

Published on: August 12, 2026

onto if f is onto

one-one if f is one-one

continuous if f is continuous

differentiable if f is differentiable

Text Solution

Verified by Experts

The correct answer is:

Given g(x) =

g(x) cannot be define where f(x) = 0 ⇒ if f(x) is onto, g(x) may or may not be onto

same argument can be given for continuity and differentiability of g(x)

if f(x) is one-one ⇒ for x 1 ≠ x 2 ⇒ f(x 1 ) ≠ f(x 2 )

g(x 1 ) ≠ g(x 2 ) ⇒ g(x) is also one-one

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