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If (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}), (f(x)=\frac{2x+3}{x-1}), what form of (x) shows that (f) is onto?यदि (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}), (f(x)=\frac{2x+3}{x-1}) है, तो (f) के आच्छादी होने के लिए (x) का रूप क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x=\frac{y+3}{y-2}\) / (x=\frac{y+3}{y-2})\(x=\frac{y+3}{y-2}\) / (x=\frac{y+3}{y-2})
Step 1: Put (\frac{2x+3}{x-1}=y). Step 2: Then (2x+3=xy-y), so (x(y-2)=y+3) and (x=\frac{y+3}{y-2}). Step 3: Since (y=2) is not in the codomain, this preimage is valid.चरण 1: (\frac{2x+3}{x-1}=y) रखें। चरण 2: (2x+3=xy-y), इसलिए (x(y-2)=y+3) और (x=\frac{y+3}{y-2})। चरण 3: चूंकि सहप्रांत में (y=2) नहीं है, यह पूर्वप्रतिबिंब मान्य रहता है।
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