JEE Main 2019MathematicsFunctionsEasyMCQ

JEE Main 2019 — Functions Question with Solution

JEE Main 2019 (09 Apr Shift 1)

Question

If the function f:R-1, -1→A defined by fx=x21-x2, is surjective, then A is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
CR-−1, 0

Step-by-step explanation

A function is surjective, when the range of the function is same as the co-domain.

Now, y=x21-x2

⇒y-yx2=x2 

⇒y=x2y+1

⇒x2=yy+1

∵  x2≥0 ⇒yy+1≥0

⇒y ∈-∞, -1∪0, ∞ or R-−1, 0.

∴ Range of f=A=R-−1, 0.

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About this question

This is a previous-year question from JEE Main 2019, 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.