Class 12 nonnegative MCQ Questions

Question 1/1 Easy Mathematics Relations and Functions Onto function Class 12 Level 25

यदि \(f:\mathbb{R}\to[2,\infty\)), (f(x)=x^-2+2) है, तो सही कथन कौन-सा है?

If \(f:\mathbb{R}\to[2,\infty\)), (f(x)=x^-2+2), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. यह आच्छादी हैIt is onto

Step 1

Concept

\(x^2\ge0\), so \(x^2+2\ge2\).

Step 2

Why this answer is correct

For every \(y\ge2\), take \(x=\sqrt{y-2}\), then (f(x)=y).

Step 3

Exam Tip

The range \([2,\infty\)) equals the codomain. चरण 1: \(x^2\ge0\), इसलिए \(x^2+2\ge2\)। चरण 2: हर \(y\ge2\) के लिए \(x=\sqrt{y-2}\) लेने पर (f(x)=y) मिलता है। चरण 3: परास \([2,\infty\)) और सहप्रांत समान हैं।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Onto function
Difficulty: Easy
Level: 25

Question Hindi:
यदि (f:\mathbb{R}\to[2,\infty)), (f(x)=x^2+2) है, तो सही कथन कौन-सा है?

Question English:
If (f:\mathbb{R}\to[2,\infty)), (f(x)=x^2+2), which statement is correct?

Options:
A. यह आच्छादी है / It is onto
B. यह आच्छादी नहीं है / It is not onto
C. यह (1) मान देता है / It gives value (1)
D. यह केवल ऋणात्मक मान देता है / It gives only negative values

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

Explanation Hindi:
चरण 1: (x^2\ge0), इसलिए (x^2+2\ge2)। चरण 2: हर (y\ge2) के लिए (x=\sqrt{y-2}) लेने पर (f(x)=y) मिलता है। चरण 3: परास ([2,\infty)) और सहप्रांत समान हैं।

Explanation English:
Step 1: (x^2\ge0), so (x^2+2\ge2). Step 2: For every (y\ge2), take (x=\sqrt{y-2}), then (f(x)=y). Step 3: The range ([2,\infty)) equals the codomain.

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nonnegative MCQ Questions for Class 12

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यदि \(f:\mathbb{R}\to[2,\infty\)), (f(x)=x^-2+2) है, तो सही कथन कौन-सा है?

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nonnegative MCQ Questions for Class 12

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यदि \(f:\mathbb{R}\to[2,\infty\)), (f(x)=x-2+2) है, तो सही कथन कौन-सा है?

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यदि \(f:\mathbb{R}\to[2,\infty\)), (f(x)=x^-2+2) है, तो सही कथन कौन-सा है?