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If (f(x)=\frac{2x+3}{x-1}), then for (x\ne1), what is (f^{-1}(x))?यदि (f(x)=\frac{2x+3}{x-1}), तो (x\ne1) के लिए (f^{-1}(x)) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{x+3}{x-2})(\frac{x+3}{x-2})
Step 1: Let (y=\frac{2x+3}{x-1}). Step 2: From (y(x-1)=2x+3), we get (x(y-2)=y+3). Step 3: Therefore (x=\frac{y+3}{y-2}), so (f^{-1}(x)=\frac{x+3}{x-2}).चरण 1: (y=\frac{2x+3}{x-1}) मानें। चरण 2: (y(x-1)=2x+3) से (x(y-2)=y+3) मिलता है। चरण 3: इसलिए (x=\frac{y+3}{y-2}), अतः (f^{-1}(x)=\frac{x+3}{x-2})।
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