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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\cos x), which statement is correct?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\cos x), तो कौन सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Neither one-one nor ontoन एकैकी न आच्छादक
Step 1: (\cos 0=1) and (\cos 2\pi=1), so the function is not one-one. Step 2: The range of (\cos x) is ([-1,1]), so it is not onto (\mathbb{R}). Step 3: If codomain is (\mathbb{R}), a bounded range function is not onto.चरण 1: (\cos 0=1) और (\cos 2\pi=1), इसलिए फलन एकैकी नहीं है। चरण 2: (\cos x) का परास ([-1,1]) है, इसलिए यह (\mathbb{R}) पर आच्छादक नहीं है। चरण 3: सहप्रांत यदि (\mathbb{R}) हो तो सीमित परास वाले फलन आच्छादक नहीं होंगे।
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