JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

f(x)=\begin{cases}2+2x, & -1\leq x<0\\ 1-\frac{x}{3}, & 0\leq x\leq 3\end{cases}

;

g(x)=\begin{cases}-x, & -3\leq x\leq 0\\ x, & 0<x\leq 1\end{cases}

, then range of

(f\circ g)(x)

(1) $[0,3)$
(2) $[0,1]$ Official answer
(3) $[0,1)$
(4) $(0,1]$

Official answer

Option 2

NTA final key.

Chapter: Relations and Functions
Topic: Functions and Domain
Idea tested: Range of Composite Functions

Same idea in other shifts

Asked 3× in all

10 Apr 2023, Shift 1 · Q1If $f(x)=\frac{(\tan 1^\circ)x+\log_e(123)}{x\log_e(1234)-(\tan 1^\circ)}$ , $x>0$ , then the least value of…HardSingle correct
26 Jun 2022, Shift 2 · Q1Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = x - 1$ and $g : \mathbb{R} - \{1, -1\} \rightarrow \mathbb{R}$ be…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.