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If A = {1, 2, 3}, B = {1, 3, 5, 7}, and f(x) = 2x − 1, what is the range of f?यदि A = {1, 2, 3}, B = {1, 3, 5, 7} और f(x) = 2x − 1 हो, तो f का परिसर क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: {1, 3, 5}{1, 3, 5}
Evaluate the function for every element of A: f(1) = 2(1) − 1 = 1, f(2) = 3, and f(3) = 5. Hence, the range of f is {1, 3, 5}. Option B is the codomain, not the range; the range contains only the values actually attained by the function. Exam tip: apply the function rule to every element of the given domain.A के प्रत्येक अवयव का मान ज्ञात करें: f(1) = 2(1) − 1 = 1, f(2) = 3 और f(3) = 5। इसलिए f का परिसर {1, 3, 5} है। विकल्प B सहपरिसर (codomain) है, जबकि परिसर केवल वास्तव में प्राप्त मानों का समुच्चय होता है। परीक्षा-युक्ति: पहले दिए गए domain के सभी अवयवों पर फलन लागू करके प्राप्त मानों को लिखें।
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