Verified Solution • 2025–26 Session moderate

QJEEM07Ma775a: JEE Main 2007 Mathematics - Class 12 JEEM07Ma775a Solution: Let f : R → R be a function defined by f ( x ) = min { x + 1 ,…

Let f:R→R be a function defined by

f(x)=min{x+1,|x|+1}, then which of the following is true?

Multiple Choice Options

  • A f(x) is differentiale everywhere
  • B f(x) is not differentiable at x = 0
  • C f(x)>1 for all x∈R
  • D f(x) is not differentiable at x = 1

Step-by-Step Verified Solution

f(x)=min{x+1,|x|+1}

⇒f(x)=x+1∀x∈R

AIEEE 2007 Mathematics - Limits, Continuity and Differentiability Question 225 English Explanation

Hence, f(x) is differentiable everywhere for all x∈R.

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