JEE Main 2017MathematicsFunctionsMediumMCQ

JEE Main 2017 — Functions Question with Solution

JEE Main 2017 (02 Apr)

Question

The function f :R→-12,12 defined as fx=x1+x2, is:

Choose an option

Show full solutionCorrect option: C
Correct answer
CSurjective but not injective

Step-by-step explanation

Let, y=x1+x2

⇒y+yx2-x=0

⇒x2y-x+y=0

⇒x=+1±  1-4y22y

⇒1-4y2 ≥0

⇒4y2 ≤1

⇒ So, y∈-12,12

Here, Co-Domain=Range

Hence, the function is surjective.

Now, for injective function

⇒x11+x12=x21+x22

⇒x1+x2x22-x2-x2x12=0

⇒x1-x2+x1x2x2-x1=0

⇒x2-x1 x1x2-1=0

⇒x2=x1 or x1=1x2

Hence, the function is not injective.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Functions chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2017, 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.