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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3-x), then (f) is not one-one. Which reason is correct?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3-x), तो (f) एकैकी नहीं है। कौन-सा कारण सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f(-1)=f(0)=f(1))(f(-1)=f(0)=f(1))
Step 1: (f(x)=x^3-x=x(x-1)(x+1)). Step 2: (f(-1)=0), (f(0)=0), and (f(1)=0), while the inputs are different. Step 3: If many inputs give the same output, the function is not one-one.चरण 1: (f(x)=x^3-x=x(x-1)(x+1))। चरण 2: (f(-1)=0), (f(0)=0), और (f(1)=0), जबकि ये आगत अलग हैं। चरण 3: एक ही निर्गत के लिए कई आगत मिलें तो फलन एकैकी नहीं होता।
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