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If (f:[0,\frac{\pi}{2}]\to[-1,1]), (f(x)=\sin x), why is (f) not onto?यदि (f:[0,\frac{\pi}{2}]\to[-1,1]), (f(x)=\sin x) है, तो (f) आच्छादी 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 ([0,\frac{\pi}{2}]), the range of (\sin x) is ([0,1]). Step 2: The codomain ([-1,1]) contains negative values, which are not obtained. Step 3: In onto questions, immediately check the effect of domain restriction.चरण 1: ([0,\frac{\pi}{2}]) पर (\sin x) का परास ([0,1]) है। चरण 2: सहप्रांत ([-1,1]) में ऋणात्मक मान भी हैं, जो नहीं मिलते। चरण 3: आच्छादीपन में प्रांत सीमित करने का प्रभाव तुरंत जांचें।
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