JEE Main 2020MathematicsFunctionsMediumMCQ

JEE Main 2020 — Functions Question with Solution

JEE Main 2020 (02 Sep Shift 1)

Question

The domain of the function f(x)=sin−1x+5x2+1 is −∞, −a∪a, ∞, then a is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C1+172

Step-by-step explanation

fx=sin−1x+5x2+1

⇒-1≤x+5x2+1≤1, ∵x∈-1,1 for sin-1x to exist.

Case 1

-x2-1≤x+5

⇒x2+1+x+5≥0, true for all x∈R.

Case 2

x+5≤x2+1

⇒x2-x-4≥0

Let x=t⇒t2-t-4≥0

⇒x+17-12x-17+12≥0

⇒x∈-∞,-17+12∪17+12,∞

∴a=1+172

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About this question

This is a previous-year question from JEE Main 2020, covering the Functions 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.