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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\frac{x^2}{1+x^2}), why is (f) not one-one?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\frac{x^2}{1+x^2}) है, तो (f) एकैकी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (f(1)=f(-1))क्योंकि (f(1)=f(-1))
Step 1: The function contains (x^2), so opposite (x)-values may give equal outputs. Step 2: (f(1)=\frac{1}{2}) and (f(-1)=\frac{1}{2}), while (1\ne-1). Step 3: For even-form rational functions, always test (x) and (-x).चरण 1: दिए गए फलन में (x^2) है, इसलिए विपरीत (x) मानों पर समान मान मिल सकता है। चरण 2: (f(1)=\frac{1}{2}) और (f(-1)=\frac{1}{2}), जबकि (1\ne-1)। चरण 3: सम रूप वाले भिन्नों में (x) और (-x) को जरूर जांचें।
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