Class 11 Mathematics - Relations and Functions - Real valued functions, domain and range of these functions Easy Quiz

Mathematics Relations and Functions Real valued functions, domain and range of these functions Easy Class 11 Level 28

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Question 1/4 Easy Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 28

यदि \(f:A\to B\) एक फलन है, तो \(A\) को क्या कहा जाता है?

If \(f:A\to B\) is a function, what is \(A\) called?

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Correct Answer

A. प्रांतDomain

Explanation

Simple Explanation

फलन \(f:A\to B\) में \(A\) उन सभी प्रारम्भिक अवयवों का समुच्चय है जिन पर फलन परिभाषित होता है, इसलिए इसे प्रांत (Domain) कहते हैं। \(B\) सहप्रांत होता है, जबकि फलन के वास्तविक मानों का समुच्चय परिसर (Range) कहलाता है और वह सहप्रांत का उपसमुच्चय हो सकता है। परीक्षा में \(f:A\to B\) लिखे होने पर पहले समुच्चय को प्रांत और दूसरे को सहप्रांत पहचानें। / In the function \(f:A\to B\), \(A\) is the set of all input elements on which the function is defined, so it is called the domain. \(B\) is the codomain, while the set of actual output values is the range, which may be a subset of the codomain. In an exam, identify the first set in \(f:A\to B\) as the domain and the second as the codomain.

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Question 2/4 Easy Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 28

फलन \(f=\{(2,4),(3,9),(4,16)\}\) का प्रांत क्या है?

What is the domain of the function \(f=\{(2,4),(3,9),(4,16)\}\)?

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Correct Answer

A. \(\{2,3,4\}\)

Explanation

Simple Explanation

किसी फलन को दर्शाने वाले क्रमित युग्मों में प्रथम अवयवों का समुच्चय प्रांत कहलाता है। यहाँ प्रथम अवयव 2, 3 और 4 हैं, इसलिए प्रांत \(\{2,3,4\}\) है। विकल्प B सह-प्रांत/परास से संबंधित है, क्योंकि उसमें द्वितीय अवयव दिए गए हैं। परीक्षा सुझाव: क्रमित युग्म \((x,y)\) में x-अवयवों से प्रांत और y-अवयवों से परास पहचानें। / The domain of a function represented by ordered pairs is the set of their first components. Here, the first components are 2, 3, and 4, so the domain is \(\{2,3,4\}\). Option B lists the second components, which form the range. Exam tip: in an ordered pair \((x,y)\), the x-values form the domain and the y-values form the range.

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Question 3/4 Easy Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 28

यदि \(f(x)=x+2\) है और इसका प्रांत \(\{1,2,3\}\) है, तो \(f(2)\) का मान क्या होगा?

If \(f(x)=x+2\) and its domain is \(\{1,2,3\}\), what is the value of \(f(2)\)?

Explanation opens after your attempt
Correct Answer

A. 4

Explanation

Simple Explanation

चूँकि \(2\) दिए गए प्रांत \(\{1,2,3\}\) का सदस्य है, इसलिए फलन में \(x=2\) रखने पर \(f(2)=2+2=4\) प्राप्त होता है। विकल्प B में केवल 3 लेने से स्थिरांक 2 जुड़ना छूट जाता है। परीक्षा में फलन का मान निकालते समय दिए गए इनपुट को सीधे \(x\) के स्थान पर रखें। / Since \(2\) belongs to the given domain \(\{1,2,3\}\), substitute \(x=2\) in the rule: \(f(2)=2+2=4\). Option B incorrectly omits the added constant 2. Exam tip: to find a function value, replace \(x\) directly with the given input.

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Question 4/4 Easy Mathematics Relations and Functions Real valued functions, domain and range of these functions Class 11 Level 28

यदि \(f(x)=x-1\) और \(A=\{2,3,4\}\) है, तो \(f(A)\) क्या होगा?

If \(f(x)=x-1\) and \(A=\{2,3,4\}\), what is \(f(A)\)?

Explanation opens after your attempt
Correct Answer

A. \(\{1,2,3\}\)

Explanation

Simple Explanation

समुच्चय \(A\) के प्रत्येक अवयव पर फलन का नियम \(f(x)=x-1\) लागू करें: \(f(2)=1\), \(f(3)=2\) और \(f(4)=3\)। इसलिए \(f(A)=\{1,2,3\}\)। विकल्प B मूल समुच्चय है, जबकि वह फलन से प्राप्त प्रतिबिंबित मानों का समुच्चय नहीं है। परीक्षा-युक्ति: किसी समुच्चय का फलन-प्रतिबिंब ज्ञात करने के लिए उसके प्रत्येक अवयव की छवि निकालें। / Apply the rule \(f(x)=x-1\) to every element of \(A\): \(f(2)=1\), \(f(3)=2\), and \(f(4)=3\). Hence, \(f(A)=\{1,2,3\}\). Option B is only the original set, not the set of images produced by the function. Exam tip: To find the image of a set, apply the function to each of its elements and collect the resulting values.

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