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If (f:(0,\infty)\to [2,\infty)), (f(x)=x+\frac{1}{x}), what type is (f)?यदि (f:(0,\infty)\to [2,\infty)), (f(x)=x+\frac{1}{x}), तो (f) कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादक है
Step 1: The minimum value of (x+\frac{1}{x}) is (2), attained at (x=1). Step 2: As (x\to0^+) or (x\to\infty), the value goes to (\infty), so all of ([2,\infty)) is obtained. Step 3: After finding the minimum, compare it with the codomain.चरण 1: (x+\frac{1}{x}) का न्यूनतम मान (2) है जो (x=1) पर मिलता है। चरण 2: (x\to0^+) या (x\to\infty) पर मान (\infty) की ओर जाता है इसलिए ([2,\infty)) पूरा मिलता है। चरण 3: न्यूनतम मान मिलने के बाद सहक्षेत्र से तुलना करें।
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