Let $f(x) = \begin{cases} -a & \text{if } -a \le x \le 0 \\ x + a & \text{if } 0 0$ and $g(x) = (f(|x|) - |f(x)|)/2$. Then the function $g : [-a, a] \to [-a, a]$ is

Option 4: neither one-one nor onto.

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2024, Shift 2, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

Let

f(x) = \begin{cases} -a & \text{if } -a \le x \le 0 \\ x + a & \text{if } 0 < x \le a \end{cases}

where

a > 0

and

g(x) = (f(|x|) - |f(x)|)/2

. Then the function

g : [-a, a] \to [-a, a]

(1)one-one.
(2)onto.
(3)both one-one and onto.
(4)neither one-one nor onto.Official answer

Official answer

Option 4

NTA final key.

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

Same topic in other shifts

All Functions and Domain questions

2 Apr 2026, Shift 1 · Q21If the domain of the function $f(x)=\sqrt{\log_{(0.6)}\left(\left|\frac{2x-5}{x^2-4}\right|\right)}$ is…HardNumerical value
4 Apr 2026, Shift 2 · Q1For the function $f:[1,\infty)\to[1,\infty)$ defined by $f(x)=(x-1)^4+1$ , among the two statements: (I) The set…HardOther
2 Apr 2025, Shift 2 · Q1If the domain of the function $f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}}$ is $(a, b)$ , then $(1+a)^2 + b^2$ is equal to :EasySingle correct
3 Apr 2025, Shift 1 · Q2If the domain of the function $f(x) = \log_e\left(\frac{2x-3}{5+4x}\right) + \sin^{-1}\left(\frac{4+3x}{2-x}\right)$ is $[\alpha, \beta)$ ,…MediumSingle correct
3 Apr 2025, Shift 2 · Q2If the domain of the function $f(x) = \log_7 (1 - \log_4 (x^2 - 9x + 18))$ is $(\alpha, \beta) \cup (\gamma, \delta)$ , then…MediumSingle correct
8 Apr 2025, Shift 2 · Q21Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of…MediumNumerical value

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.