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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\sin x), why is (f) not onto?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\sin x), तो (f) आच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because the range is ([-1,1]) and the codomain is (\mathbb{R})क्योंकि परास ([-1,1]) है और सहप्रांत (\mathbb{R}) है
Step 1: The range of (\sin x) is ([-1,1]). Step 2: The codomain (\mathbb{R}) contains values such as (2), which are never obtained. Step 3: For trigonometric functions, remembering the range is very important for onto checking.चरण 1: (\sin x) का परास ([-1,1]) होता है। चरण 2: सहप्रांत (\mathbb{R}) में (2) जैसे मान हैं, जो कभी प्राप्त नहीं होते। चरण 3: त्रिकोणमितीय फलनों में परास याद रखना आच्छादकता के लिए बहुत जरूरी है।
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