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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3-3x), which is a correct proof that it is not one-one?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3-3x), तो एकैकी न होने का सही प्रमाण कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f(0)=f(\sqrt{3})=0)(f(0)=f(\sqrt{3})=0)
Step 1: (f(0)=0^3-3\cdot0=0). Step 2: (f(\sqrt{3})=(\sqrt{3})^3-3\sqrt{3}=3\sqrt{3}-3\sqrt{3}=0). Step 3: Two distinct inputs have the same image, so the function is not one-one.चरण 1: (f(0)=0^3-3\cdot0=0)। चरण 2: (f(\sqrt{3})=(\sqrt{3})^3-3\sqrt{3}=3\sqrt{3}-3\sqrt{3}=0)। चरण 3: दो अलग आगतों का समान प्रतिबिंब मिल गया, इसलिए फलन एकैकी नहीं है।
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