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If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=\frac{x+1}{2}), choose the correct conclusion for (f).यदि (f:\mathbb{R}\to\mathbb{R}) और (f(x)=\frac{x+1}{2}) है, तो (f) के लिए सही निष्कर्ष चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: One-oneएकैकी है
Step 1: Assume (f(a)=f(b)). Step 2: From (\frac{a+1}{2}=\frac{b+1}{2}), we get (a+1=b+1), so (a=b). Step 3: Even in fractional form, a linear function with non-zero coefficient is one-one.चरण 1: मान लें (f(a)=f(b))। चरण 2: (\frac{a+1}{2}=\frac{b+1}{2}) से (a+1=b+1), इसलिए (a=b)। चरण 3: भिन्न रूप में भी गैर-शून्य गुणांक वाला रैखिक फलन एकैकी होता है।
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