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If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x^3-3x), why is (f) not one-one?यदि (f:\mathbb{R}\to\mathbb{R}) और (f(x)=x^3-3x), तो (f) एकैकी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (f(0)=f(\sqrt{3}))क्योंकि (f(0)=f(\sqrt{3}))
Step 1: (f(0)=0). Step 2: (f(\sqrt{3})=(\sqrt{3})^3-3\sqrt{3}=3\sqrt{3}-3\sqrt{3}=0), while (0\neq \sqrt{3}). Step 3: If two distinct inputs give the same image, the function is not one-one.चरण 1: (f(0)=0) है। चरण 2: (f(\sqrt{3})=(\sqrt{3})^3-3\sqrt{3}=3\sqrt{3}-3\sqrt{3}=0), जबकि (0\neq \sqrt{3})। चरण 3: दो अलग इनपुट की समान छवि मिलने पर फलन एकैकी नहीं होता।
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