JEE Main 2019MathematicsFunctionsMediumMCQ

JEE Main 2019 — Functions Question with Solution

JEE Main 2019 (09 Jan Shift 2)

Question

Let A=  { x∈R:x is not a positive integer} . Define a function  f:A→R as fx=2xx-1 , then f is:

Choose an option

Show full solutionCorrect option: A
Correct answer
AInjective but not surjective

Step-by-step explanation

Given, function fx=2xx-1 and domain of fx is -∞, 0

Now f'x=x-12-2x1-0x-12

f′x=-2x-12<0

⇒f is always decreasing in the given domain.



Clearly, given function is one-one or injective.
Since, codomain -∞, ∞≠ Range 0, 2 , hence f is into.

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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.