JEE Main 2016MathematicsContinuity and DifferentiabilityMediumMCQ

JEE Main 2016 — Continuity and Differentiability Question with Solution

JEE Main 2016 (03 Apr)

Question

For x∈R,fx=log⁡2-sin⁡x and gx=ffx, then

Choose an option

Show full solutionCorrect option: D
Correct answer
Dg'0=cos⁡log⁡2

Step-by-step explanation

In the neighborhood of x=0, fx=log⁡2-sin⁡x

∴ gx=f(fx)=log⁡2-sin⁡fx

=log⁡2-sin log⁡2-sin⁡x

∴ g′x=-cos⁡log⁡2-sin⁡x –cos⁡x

∴ g′0=cos⁡log⁡2

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About this question

This is a previous-year question from JEE Main 2016, 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.