यदि \(f:\mathbb{R}\to\mathbb{R}\) को (f(x)=\frac{x}{1+x-2}) से परिभाषित किया गया है, तो (f) एकैकी नहीं है। सही कारण कौन सा है?
If \(f:\mathbb{R}\to\mathbb{R}\) is defined by (f(x)=\frac{x}{1+x-2}), why is (f) not one-one?
Explanation opens after your attempt
Correct Answer
A. क्योंकि (f(2)=f\left\(\frac{1}{2}\right\))Because (f(2)=f\left\(\frac{1}{2}\right\))
Concept
(f(2)=\frac{2}{1+4}=\frac{2}{5}).
Why this answer is correct
(f\left\(\frac{1}{2}\right\)=\frac{\frac{1}{2}}{1+\frac{1}{4}}=\frac{\frac{1}{2}}{\frac{5}{4}}=\frac{2}{5}).
Exam Tip
Once two distinct inputs have the same image, the function is not one-one. चरण 1: (f(2)=\frac{2}{1+4}=\frac{2}{5})। चरण 2: (f\left\(\frac{1}{2}\right\)=\frac{\frac{1}{2}}{1+\frac{1}{4}}=\frac{\frac{1}{2}}{\frac{5}{4}}=\frac{2}{5})। चरण 3: दो अलग निवेशों का समान प्रतिबिंब मिलते ही फलन एकैकी नहीं रहता।
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