JEE Main 2019MathematicsFunctionsMediumMCQ

JEE Main 2019 — Functions Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

Let fx=x2, x∈R . For any A⊆R, define gA={x∈R :f(x)∈A} . If S=[0, 4] , then which one of the following statements is not true?

Choose an option

Show full solutionCorrect option: D
Correct answer
DgfS=gS

Step-by-step explanation

From the given information we can conclude
gS=-2,2 , So, f(g(S))=0, 4=S
And f(S)=0, 16⇒fgS≠fS
Also, gfS=-4, 4≠gS
So, gfS≠S
Hence, gfS=gS is not true.

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 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.