Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions

Class 12 Maths · Relations And Functions · Mcq Single Correct #58

Let \(f,g:\mathbb{R}\to\mathbb{R}\) be defined by \(f(x)=\begin{cases}0,&x\in\mathbb{Q}\\x,&x\notin\mathbb{Q}\end{cases}\) and \(g(x)=\begin{cases}0,&x\notin\mathbb{Q}\\x,&x\in\mathbb{Q}\end{cases}\). Then \((f-g)(x)\) is

(A) One-one and onto
(B) Neither one-one nor onto
(C) One-one but not onto
(D) Onto but not one-one

✅ Step-by-Step Solution

Final Answer: Option (A): One-one and onto

\(h=f-g\) equals \(-x\) on rationals and \(x\) on irrationals. It preserves the rational/irrational partition and \(h(h(x))=x\). Thus \(h\) is its own inverse and is bijective.

Master Chapter 1: Relations And Functions

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Relations And Functions.

📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →

← Previous Question

Let \(R\) be the relation on \(\mathbb{R}\) defined by \(aRb\) if…

Next Question →

For real \(x\), let \(f(x)=x^3+5x+1\). Then

Class 12 Maths · Relations And Functions · Mcq Single Correct #58

✅ Step-by-Step Solution

Master Chapter 1: Relations And Functions

More Practice Questions in Relations And Functions

Related Questions in Relations And Functions