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If (f:(-\frac{\pi}{2},\frac{\pi}{2})\to[-1,1]), (f(x)=\sin x), what is the correct conclusion?यदि (f:(-\frac{\pi}{2},\frac{\pi}{2})\to[-1,1]), (f(x)=\sin x), तो सही निष्कर्ष क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is not onto because (-1) and (1) are not obtainedयह आच्छादक नहीं है क्योंकि (-1) और (1) प्राप्त नहीं होते
Step 1: The open interval does not include (x=\pm\frac{\pi}{2}). Step 2: Hence the range of (\sin x) is ((-1,1)), while the codomain is ([-1,1]). Step 3: The difference between open and closed intervals can decide onto status.चरण 1: खुले अंतराल में (x=\pm\frac{\pi}{2}) शामिल नहीं हैं। चरण 2: इसलिए (\sin x) का परास ((-1,1)) है, जबकि सहप्रांत ([-1,1]) है। चरण 3: खुले और बंद अंतराल का फर्क आच्छादकता में निर्णायक हो सकता है।
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