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If (f:\mathbb{R}\to(0,\infty)) is given by (f(x)=e^{2x+1}), what is (f^{-1}(x))?यदि (f:\mathbb{R}\to(0,\infty)) को (f(x)=e^{2x+1}) से दिया गया है, तो (f^{-1}(x)) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{\ln x-1}{2})(\frac{\ln x-1}{2})
Step 1: Put (y=e^{2x+1}). Step 2: Then (\ln y=2x+1), so (x=\frac{\ln y-1}{2}). Step 3: Replacing (y) by (x) gives (f^{-1}(x)=\frac{\ln x-1}{2}).चरण 1: (y=e^{2x+1}) मानें। चरण 2: (\ln y=2x+1), इसलिए (x=\frac{\ln y-1}{2})। चरण 3: चर बदलकर (f^{-1}(x)=\frac{\ln x-1}{2}) मिलता है।
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