JEE Main 2019 — Functions Question with Solution
From: JEE Main 2019 (Online) 9th January Evening Slot
Question
Let A = {x R : x is not a positive integer}.
Define a function : A R as = ,
then is :
Define a function : A R as = ,
then is :
Choose an option
Show full solutionCorrect option: D
Correct answer
Dinjective but not surjective
Step-by-step explanation
f(x) =
f(x) = 2 +
f'(x) = < 0 x R
Hence f(x) is strictly decreasing
So, f(x) is one-one
Range : Let y =
xy y = 2x
x(y 2) = y
x =
given that x R : x is not a +ve integer
N (N Natural number)
y Ny 2N
y
So range R (in to function)
f(x) = 2 +
f'(x) = < 0 x R
Hence f(x) is strictly decreasing
So, f(x) is one-one
Range : Let y =
xy y = 2x
x(y 2) = y
x =
given that x R : x is not a +ve integer
N (N Natural number)
y Ny 2N
y
So range R (in to function)
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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.