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

Published by: CGP EDU Academic Team

Published on: August 12, 2026

Let f(x) = | x − − 1|. Then

f(x 2 ) = (f(x)) 2

f(x + y) = f(x) + f(y)

f(|x|) = |f(x)|

None of these

Text Solution

Verified by Experts

The correct answer is:

f(x) = |x – 1| =

Consider f(x 2 ) = (f(x)) 2

If it is true it should be true x ∴ ∴ Put x = 2

LHS = f(2 2 ) = | 4 − − 1| = 3

RHS = f((2) 2 ) = 1

∴ ∴ is not correct

Consider f(x + y) = f(x) + f(y)

Put x = 2, y = 5 we get

F(7) = 6; f(2) + f(5) = 1 + 4 = 5 ∴ ∴ is not correct.

Consider f(|x|) = |f(x)|

Put x = − − 5 then f(| − − 5|) = f(5) = 4

|f( − − 5)| = | − − 5 − − 1| = 6

∴ ∴ is not correct.

Hence is the correct alternative

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