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If (f:\mathbb{R}\setminus{2}\to\mathbb{R}\setminus{3}) is given by (f(x)=\frac{3x+1}{x-2}), what is (f^{-1}(x))?यदि (f:\mathbb{R}\setminus{2}\to\mathbb{R}\setminus{3}) को (f(x)=\frac{3x+1}{x-2}) से दिया गया है, तो (f^{-1}(x)) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{2x+1}{x-3})(\frac{2x+1}{x-3})
Step 1: Put (y=\frac{3x+1}{x-2}) and isolate (x). Step 2: From (y(x-2)=3x+1), we get (x(y-3)=2y+1). Step 3: Hence (x=\frac{2y+1}{y-3}), and replacing (y) by (x) gives the inverse.चरण 1: (y=\frac{3x+1}{x-2}) मानकर (x) को अलग करें। चरण 2: (y(x-2)=3x+1) से (x(y-3)=2y+1) मिलता है। चरण 3: इसलिए (x=\frac{2y+1}{y-3}), और चर बदलने पर प्रतिलोम मिल जाता है।
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