Let f : → R and g : → R be functions defined by f(x) = [x…

Maths Functions, Limits, Continuity and Differentiability JEE (Advamced) / IIT - JEE Problems ( Previous Year ) Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

Let f : → R and g : → R be functions defined by f(x) = [x 2 – 3] and

g(x) = |x| f(x) + |4x – 7| f(x), where [y] denotes the greatest integer less than or equal to y for y ∈ R. Then

f is discontinuous exactly at three points in

f is discontinuous exactly at four point in

g is NOT differentiable exactly at four points in

g is NOT differentiable exactly at five points in

Text Solution

Verified by Experts

The correct answer is:

(b,c)

Sol. f(x) = [x 2 – 3] = [x 2 ] – 3 =

g(x) = |x| f(x) + |4x–7| f(x)

= (|x| + |4x – 7|) [x 2 – 3] =

Now graph of given function is

f(x) g(x)

Clearly F is not discontinuous at exactly 4 point in [–1/2, 2] and g is not differentiable at 4 points in (–1/2, 2) Hence Ans. is BC

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