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If (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) and (f(x)=\frac{2x+1}{x-1}), is (f) onto or not?यदि (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) और (f(x)=\frac{2x+1}{x-1}), तो (f) सर्वाच्छादक है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is ontoसर्वाच्छादक है
Step 1: Put (y=\frac{2x+1}{x-1}), which gives (x=\frac{y+1}{y-2}). Step 2: Since the codomain has (y\ne2), this (x) is defined and also (x\ne1). Step 3: For rational functions, solve for (x) in terms of (y) to test onto.चरण 1: (y=\frac{2x+1}{x-1}) मानकर (x=\frac{y+1}{y-2}) मिलता है। चरण 2: सहप्रांत में (y\ne2), इसलिए यह (x) परिभाषित है और (x\ne1) भी रहता है। चरण 3: भिन्नात्मक फलन में (x) को (y) के रूप में निकालना सबसे सुरक्षित तरीका है।
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