Class 12 sine transformation MCQ Questions

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

फलन \(f:\mathbb{R}\to[0,2]\), (f(x)=1+\sin x), सर्वाच्छादक क्यों है?

Why is \(f:\mathbb{R}\to[0,2]\), (f(x)=1+\sin x), onto?

Explanation opens after your attempt

Correct Answer

A. क्योंकि \(\sin x\) का परास ([-1,1]) है, इसलिए \(1+\sin x\) का परास ([0,2]) हैBecause the range of \(\sin x\) is ([-1,1]), so the range of \(1+\sin x\) is ([0,2])

Step 1

Concept

Values of \(\sin x\) run from (-1) to (1).

Step 2

Why this answer is correct

Adding (1) changes the range to ([0,2]), equal to the codomain.

Step 3

Exam Tip

Apply vertical shifts clearly while finding the range. चरण 1: \(\sin x\) के मान (-1) से (1) तक होते हैं। चरण 2: उसमें (1) जोड़ने पर परास ([0,2]) बनता है, जो सहप्रांत के बराबर है। चरण 3: परास पर ऊर्ध्व स्थानांतरण का प्रभाव साफ-साफ लगाएँ।

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

Question Hindi:
फलन (f:\mathbb{R}\to[0,2]), (f(x)=1+\sin x), सर्वाच्छादक क्यों है?

Question English:
Why is (f:\mathbb{R}\to[0,2]), (f(x)=1+\sin x), onto?

Options:
A. क्योंकि (\sin x) का परास ([-1,1]) है, इसलिए (1+\sin x) का परास ([0,2]) है / Because the range of (\sin x) is ([-1,1]), so the range of (1+\sin x) is ([0,2])
B. क्योंकि (\sin x) सभी वास्तविक मान देता है / Because (\sin x) gives all real values
C. क्योंकि (1+\sin x) कभी (0) नहीं देता / Because (1+\sin x) never gives (0)
D. क्योंकि (1+\sin x) केवल (1) देता है / Because (1+\sin x) gives only (1)

Correct Answer:
A. क्योंकि (\sin x) का परास ([-1,1]) है, इसलिए (1+\sin x) का परास ([0,2]) है / Because the range of (\sin x) is ([-1,1]), so the range of (1+\sin x) is ([0,2])

Explanation Hindi:
चरण 1: (\sin x) के मान (-1) से (1) तक होते हैं। चरण 2: उसमें (1) जोड़ने पर परास ([0,2]) बनता है, जो सहप्रांत के बराबर है। चरण 3: परास पर ऊर्ध्व स्थानांतरण का प्रभाव साफ-साफ लगाएँ।

Explanation English:
Step 1: Values of (\sin x) run from (-1) to (1). Step 2: Adding (1) changes the range to ([0,2]), equal to the codomain. Step 3: Apply vertical shifts clearly while finding the range.

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sine transformation MCQ Questions for Class 12

Practice Questions

फलन \(f:\mathbb{R}\to[0,2]\), (f(x)=1+\sin x), सर्वाच्छादक क्यों है?

Concept

Why this answer is correct

Exam Tip

sine transformation Revision Links

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sine transformation MCQ Questions for Class 12

Practice Questions

फलन \(f:\mathbb{R}\to[0,2]\), (f(x)=1+\sin x), सर्वाच्छादक क्यों है?

Concept

Why this answer is correct

Exam Tip

sine transformation Revision Links

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All Subjects

Search sine transformation

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