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If \(f:\left[0,\frac{\pi}{2}\right]\to[-1,1]\), \(f(x)=\sin x\), why is (f) not onto?यदि \(f:\left[0,\frac{\pi}{2}\right]\to[-1,1]\), \(f(x)=\sin x\), तो (f) सर्वाच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because negative values are not obtainedक्योंकि ऋणात्मक मान नहीं मिलते
Step 1: On \(\left[0,\frac{\pi}{2}\right]\), the range of (\sin x) is ([0,1]). Step 2: The codomain ([-1,1]) also contains negative values, which are not images. Step 3: Along with the standard range, find the range on the given domain.चरण 1: \(\left[0,\frac{\pi}{2}\right]\) पर (\sin x) का परास ([0,1]) है। चरण 2: सहप्रांत ([-1,1]) में ऋणात्मक मान भी हैं, जो छवि नहीं बनते। चरण 3: पूरा मानक परास याद करने के साथ-साथ दिए गए प्रांत पर परास निकालें।
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