Class 12 odd degree polynomial MCQ Questions

Question 1/1 Hard Mathematics Relations and Functions Onto function Class 12 Level 27

फलन \(f:\mathbb{R}\to\mathbb{R}\) जहाँ (f(x)=x^-3-3x), क्या सर्वाच्छादक है?

Is the function \(f:\mathbb{R}\to\mathbb{R}\), where (f(x)=x^-3-3x), onto?

Explanation opens after your attempt

Correct Answer

A. हाँ क्योंकि यह विषम घात का सतत बहुपद है और दोनों दिशाओं में असीमित जाता हैYes because it is a continuous odd-degree polynomial and is unbounded in both directions

Step 1

Concept

\(x^3-3x\) is continuous.

Step 2

Why this answer is correct

As \(x\to\infty\), it goes to \(\infty\), and as \(x\to-\infty\), it goes to \(-\infty\).

Step 3

Exam Tip

Even with turning points, end behavior can show onto property. चरण 1: \(x^3-3x\) सतत है। चरण 2: \(x\to\infty\) पर मान \(\infty\) की ओर और \(x\to-\infty\) पर \(-\infty\) की ओर जाता है। चरण 3: स्थानीय मोड़ होने पर भी अंत व्यवहार सर्वाच्छादकता दिखा सकता है।

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

Question Hindi:
फलन (f:\mathbb{R}\to\mathbb{R}) जहाँ (f(x)=x^3-3x), क्या सर्वाच्छादक है?

Question English:
Is the function (f:\mathbb{R}\to\mathbb{R}), where (f(x)=x^3-3x), onto?

Options:
A. हाँ क्योंकि यह विषम घात का सतत बहुपद है और दोनों दिशाओं में असीमित जाता है / Yes because it is a continuous odd-degree polynomial and is unbounded in both directions
B. नहीं क्योंकि इसका न्यूनतम मान (0) है / No because its minimum value is (0)
C. नहीं क्योंकि इसका अधिकतम मान (3) है / No because its maximum value is (3)
D. नहीं क्योंकि यह केवल धनात्मक मान देता है / No because it gives only positive values

Correct Answer:
A. हाँ क्योंकि यह विषम घात का सतत बहुपद है और दोनों दिशाओं में असीमित जाता है / Yes because it is a continuous odd-degree polynomial and is unbounded in both directions

Explanation Hindi:
चरण 1: (x^3-3x) सतत है। चरण 2: (x\to\infty) पर मान (\infty) की ओर और (x\to-\infty) पर (-\infty) की ओर जाता है। चरण 3: स्थानीय मोड़ होने पर भी अंत व्यवहार सर्वाच्छादकता दिखा सकता है।

Explanation English:
Step 1: (x^3-3x) is continuous. Step 2: As (x\to\infty), it goes to (\infty), and as (x\to-\infty), it goes to (-\infty). Step 3: Even with turning points, end behavior can show onto property.

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odd degree polynomial MCQ Questions for Class 12

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फलन \(f:\mathbb{R}\to\mathbb{R}\) जहाँ (f(x)=x^-3-3x), क्या सर्वाच्छादक है?

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odd degree polynomial MCQ Questions for Class 12

Practice Questions

फलन \(f:\mathbb{R}\to\mathbb{R}\) जहाँ (f(x)=x-3-3x), क्या सर्वाच्छादक है?

Concept

Why this answer is correct

Exam Tip

odd degree polynomial Revision Links

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फलन \(f:\mathbb{R}\to\mathbb{R}\) जहाँ (f(x)=x^-3-3x), क्या सर्वाच्छादक है?