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If (f:(0,\infty)\to \mathbb{R}), (f(x)=x-\frac{1}{x}), what is the correct conclusion about (f)?यदि (f:(0,\infty)\to \mathbb{R}), (f(x)=x-\frac{1}{x}), तो (f) के लिए सही निष्कर्ष क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादक है
Step 1: As (x\to0^+), (x-\frac{1}{x}\to-\infty). Step 2: As (x\to\infty), (x-\frac{1}{x}\to\infty), and the function is continuous. Step 3: For open-domain questions, use limits at the ends to understand the range.चरण 1: (x\to0^+) पर (x-\frac{1}{x}\to-\infty) होता है। चरण 2: (x\to\infty) पर (x-\frac{1}{x}\to\infty) होता है और फलन सतत है। चरण 3: खुले प्रांत वाले प्रश्नों में सिरों पर सीमा देखकर परास समझें।
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