Class 12 am gm MCQ Questions

Question 1/1 Expert Mathematics Relations and Functions Functions Class 12 Level 19

यदि (f:\(0,\infty\)\to\mathbb{R}) को (f(x)=x+\frac{1}{x}) से दिया गया है, तो (f) का परास क्या है?

If (f:\(0,\infty\)\to\mathbb{R}) is given by (f(x)=x+\frac{1}{x}), what is the range of (f)?

Explanation opens after your attempt

Correct Answer

A. \([2,\infty\))

Step 1

Concept

For positive (x), \(x+\frac{1}{x}\geq2\).

Step 2

Why this answer is correct

At (x=1), the value (2) is attained.

Step 3

Exam Tip

The AM-GM idea is very useful for such range questions. चरण 1: धनात्मक (x) के लिए \(x+\frac{1}{x}\geq2\) होता है। चरण 2: (x=1) पर मान (2) मिल जाता है। चरण 3: ऐसे प्रश्न में गुणोत्तर और अंकगणितीय माध्य का विचार बहुत उपयोगी है।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Functions
Difficulty: Expert
Level: 19

Question Hindi:
यदि (f:(0,\infty)\to\mathbb{R}) को (f(x)=x+\frac{1}{x}) से दिया गया है, तो (f) का परास क्या है?

Question English:
If (f:(0,\infty)\to\mathbb{R}) is given by (f(x)=x+\frac{1}{x}), what is the range of (f)?

Options:
A. ([2,\infty))
B. ((2,\infty))
C. (\mathbb{R})
D. ((-\infty,2])

Correct Answer:
A. ([2,\infty))

Explanation Hindi:
चरण 1: धनात्मक (x) के लिए (x+\frac{1}{x}\geq2) होता है। चरण 2: (x=1) पर मान (2) मिल जाता है। चरण 3: ऐसे प्रश्न में गुणोत्तर और अंकगणितीय माध्य का विचार बहुत उपयोगी है।

Explanation English:
Step 1: For positive (x), (x+\frac{1}{x}\geq2). Step 2: At (x=1), the value (2) is attained. Step 3: The AM-GM idea is very useful for such range questions.

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am gm MCQ Questions for Class 12

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यदि (f:\(0,\infty\)\to\mathbb{R}) को (f(x)=x+\frac{1}{x}) से दिया गया है, तो (f) का परास क्या है?

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am gm MCQ Questions for Class 12

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यदि (f:\(0,\infty\)\to\mathbb{R}) को (f(x)=x+\frac{1}{x}) से दिया गया है, तो (f) का परास क्या है?

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