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Why is (f:\mathbb{R}\to[-1,1]), (f(x)=\frac{2}{\pi}\tan^{-1}x), not onto?फलन (f:\mathbb{R}\to[-1,1]), (f(x)=\frac{2}{\pi}\tan^{-1}x), सर्वाच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (-1) and (1) are not obtainedक्योंकि (-1) और (1) नहीं मिलते
Step 1: (\tan^{-1}x) never equals (\frac{\pi}{2}) or (-\frac{\pi}{2}). Step 2: After multiplying, (1) and (-1) are only limiting values, not actual images. Step 3: The difference between open and closed intervals can decide onto property.चरण 1: (\tan^{-1}x) कभी (\frac{\pi}{2}) या (-\frac{\pi}{2}) नहीं होता। चरण 2: इसलिए गुणा करने के बाद (1) और (-1) केवल सीमा मान हैं, वास्तविक छवि नहीं। चरण 3: खुले और बंद अंतराल का अंतर सर्वाच्छादकता में निर्णायक हो सकता है।
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