JEE Main 2023MathematicsContinuity and DifferentiabilityMediumMCQ

JEE Main 2023 — Continuity and Differentiability Question with Solution

JEE Main 2023 (11 Apr Shift 2)

Question

Let f and g be two functions defined by fx=x+1,      x<0x-1,  x≥0and gx=x+1,      x<01,            x≥0.Then gofx is

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Show full solutionCorrect option: A
Correct answer
AContinuous everywhere but not differentiable exactly at one point

Step-by-step explanation

Given,

fx=x+1,      x<0x-1,  x≥0and gx=x+1,      x<01,            x≥0

⇒fx=x+1,x<01-x,0≤x<1x-1,x>1& gx=1+x,x<01,x≥0
     

Now, for gofx 

 gofx=1+fx,fx<0, x<01,fx≥0, x≥0

⇒ gofx=x+2,x<-11,x≥-1

Now plotting the diagram we get,

Now from above diagram we can say that function is continuous but not differentiable at x=-1 due to sharp corner.

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About this question

This is a previous-year question from JEE Main 2023, covering the Continuity and Differentiability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.