Let f(x) and g(x) be defined by f(x) = [x] and g(x) = (whe…

Maths Functions, Limits, Continuity and Differentiability General More Than One Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 11, 2026

Let f(x) and g(x) be defined by f(x) = [x] and g(x) = (where [ . ] denotes the greatest integer function), then

g(x) exists, but g is not continuous at x = 1

f(x) does not exist and f is not continuous at x = 1

gof is continuous for all x

fog is continuous for all x

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a,b,c)f(x) = [x] and g(x) =

, but g(1) = 0

does not exist since LHL = 0 and RHL = 1

gof(x) = g([x]) = 0 gof(x) is continous for all values of x

fog =

fog(1) = 0 , ,

fog is not continous at x = 1

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