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If (f:[0,\frac{\pi}{3}]\to[-1,1]), (f(x)=\cos x), why is it not onto?यदि (f:[0,\frac{\pi}{3}]\to[-1,1]), (f(x)=\cos x) है, तो यह 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}{3}]), the range of (\cos x) is ([\frac{1}{2},1]). Step 2: The codomain ([-1,1]) contains negative values, which are not obtained. Step 3: When the domain is restricted, the range must be checked again.चरण 1: ([0,\frac{\pi}{3}]) पर (\cos x) का परास ([\frac{1}{2},1]) है। चरण 2: सहप्रांत ([-1,1]) में ऋणात्मक मान भी हैं, जो नहीं मिलते। चरण 3: प्रांत सीमित करते समय परास को फिर से जांचना चाहिए।
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