NCERT Class 12 · Ch 1 Exercise 1.2 · Q4
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.2 Question 4
Prove that f:ℝ→ℝ, f(x)=|x|, is neither one-one nor onto.
💡 Concept Hints
- Compare opposite inputs and determine whether negative outputs are possible.
- Separate the one-one and onto claims. For onto, ensure each inverse candidate lies in the allowed domain.
✅ Step-by-Step Solution
Final Answer: Neither injective nor surjective.
- f(1)=f(−1)=1 with distinct inputs, so f is not injective.
- For every x, |x|≥0. Conversely any y≥0 is reached by x=y, so the range is [0,∞).
- The negative number −1 in the codomain ℝ is not reached, so f is not onto.
Master Chapter 1: Relations And Functions
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Relations And Functions.
← Previous Question
Prove that f:ℝ→ℝ, f(x)=⌊x⌋, is neither one-one nor onto.
Next Question →Prove that the signum function f:ℝ→ℝ, with f(x)=1 for x>0, f(0)=0…
Related Questions in Relations And Functions
Class 12 Relations And Functions · Mcq Single Correct
Given the relation \(R=\{(1,2),(2,3)\}\) on the set \(A=\{1,2,3\}\), the minimum number of…
Class 12 Relations And Functions · Mcq Single Correct
The function \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=e^x\) is
Class 12 Relations And Functions · Mcq Single Correct
If \(f:\mathbb{R}\to\mathbb{R}\)…
Class 12 Relations And Functions · Mcq Single Correct
If \(f:\mathbb{R}\to S\), defined by \(f(x)=\sin x-\sqrt{3}\cos x+1\), is onto, then the…
Class 12 Relations And Functions · Mcq Single Correct
Let \(A=\{1,2,3\}\) and \(B=\{a,b,c\}\). Then the number of bijective functions from \(A\) to…
Class 12 Relations And Functions · Mcq Single Correct
Let \(A\) and \(B\) be two finite sets having \(m\) and \(n\) elements respectively. Then the…