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The function (f:(0,\infty)\to\mathbb{R}), (f(x)=x-\frac{1}{x}), is onto becauseफलन (f:(0,\infty)\to\mathbb{R}), (f(x)=x-\frac{1}{x}), सर्वाच्छादक है क्योंकि
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is continuous and tends to (-\infty) as (x\to0^+), and to (\infty) as (x\to\infty)यह सतत है और (x\to0^+) पर (-\infty), (x\to\infty) पर (\infty) की ओर जाता है
Step 1: On ((0,\infty)), (x-\frac{1}{x}) is continuous. Step 2: As (x\to0^+), it tends to (-\infty), and as (x\to\infty), it tends to (\infty). Step 3: A continuous function crossing all real values gives onto property.चरण 1: ((0,\infty)) पर (x-\frac{1}{x}) सतत है। चरण 2: (x\to0^+) पर मान (-\infty) की ओर और (x\to\infty) पर (\infty) की ओर जाता है। चरण 3: सतत फलन यदि दोनों छोरों पर सभी वास्तविक मानों को पार करे, तो सर्वाच्छादकता मिलती है।
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