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Question Expert Mathematics Relations and Functions Onto function Class 12 Level 27

यदि \(f:\mathbb{N}\to{n\in\mathbb{N}:n\ge4}\) जहाँ (f(n)=n+3), तो (f) के बारे में सही कथन चुनिए।

If \(f:\mathbb{N}\to{n\in\mathbb{N}:n\ge4}\), where (f(n)=n+3), choose the correct statement about (f).

Explanation opens after your attempt

Correct Answer

A. यह आच्छादी हैIt is onto

Step 1

Concept

The first value of (f(n)=n+3) is (4).

Step 2

Why this answer is correct

For every \(y\ge4\), (n=y-3) is a natural number.

Step 3

Exam Tip

In onto proofs, take an arbitrary (y) and find its preimage. चरण 1: (f(n)=n+3) का पहला मान (4) है। चरण 2: हर \(y\ge4\) के लिए (n=y-3) प्राकृतिक संख्या है। चरण 3: आच्छादिता में (y) लेकर उसका पूर्वप्रतिबिंब निकालना मजबूत तरीका है।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Onto function
Difficulty: Expert
Level: 27

Question Hindi:
यदि (f:\mathbb{N}\to{n\in\mathbb{N}:n\ge4}) जहाँ (f(n)=n+3), तो (f) के बारे में सही कथन चुनिए।

Question English:
If (f:\mathbb{N}\to{n\in\mathbb{N}:n\ge4}), where (f(n)=n+3), choose the correct statement about (f).

Options:
A. यह आच्छादी है / It is onto
B. यह आच्छादी नहीं है / It is not onto
C. यह केवल (4) नहीं देता / It misses only (4)
D. यह केवल (1) देता है / It gives only (1)

Correct Answer:
A. यह आच्छादी है / It is onto

Explanation Hindi:
चरण 1: (f(n)=n+3) का पहला मान (4) है। चरण 2: हर (y\ge4) के लिए (n=y-3) प्राकृतिक संख्या है। चरण 3: आच्छादिता में (y) लेकर उसका पूर्वप्रतिबिंब निकालना मजबूत तरीका है।

Explanation English:
Step 1: The first value of (f(n)=n+3) is (4). Step 2: For every (y\ge4), (n=y-3) is a natural number. Step 3: In onto proofs, take an arbitrary (y) and find its preimage.

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यदि \(f:\mathbb{N}\to{n\in\mathbb{N}:n\ge4}\) जहाँ (f(n)=n+3), तो (f) के बारे में सही कथन चुनिए।

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