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If (f:[0,\frac{\pi}{6}]\to[0,1]), (f(x)=\sin x), why is it not onto?यदि (f:[0,\frac{\pi}{6}]\to[0,1]), (f(x)=\sin x) है, तो यह आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because a value like (\frac{3}{4}) is not obtainedक्योंकि (\frac{3}{4}) जैसा मान नहीं मिलता
Step 1: On ([0,\frac{\pi}{6}]), the range of (\sin x) is ([0,\frac{1}{2}]). Step 2: The codomain ([0,1]) contains (\frac{3}{4}), which is not in the range. Step 3: On a small trigonometric interval, the range can also be small.चरण 1: ([0,\frac{\pi}{6}]) पर (\sin x) का परास ([0,\frac{1}{2}]) है। चरण 2: सहप्रांत ([0,1]) में (\frac{3}{4}) है, पर वह परास में नहीं आता। चरण 3: छोटे त्रिकोणमितीय अंतराल पर परास भी छोटा हो सकता है।
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