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If (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) is defined by (f(x)=\frac{2x+3}{x-1}), what is (f^{-1}(x))?यदि (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) को (f(x)=\frac{2x+3}{x-1}) से परिभाषित किया गया है, तो (f^{-1}(x)) क्या होगा?
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: Then (yx-y=2x+3), so (x(y-2)=y+3) and (x=\frac{y+3}{y-2}). Step 3: Replacing (y) by (x), we get (f^{-1}(x)=\frac{x+3}{x-2}).चरण 1: (y=\frac{2x+3}{x-1}) मानें। चरण 2: (yx-y=2x+3), इसलिए (x(y-2)=y+3) और (x=\frac{y+3}{y-2})। चरण 3: अब (y) की जगह (x) लिखने पर (f^{-1}(x)=\frac{x+3}{x-2}) मिलता है।
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