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If (f:(0,\infty)\to\mathbb{R}) is defined by (f(x)=\ln x), what is (f^{-1}(x))?यदि (f:(0,\infty)\to\mathbb{R}) को (f(x)=\ln x) से परिभाषित किया गया है, तो (f^{-1}(x)) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (e^x)(e^x)
Step 1: Let (y=\ln x). Step 2: By the definition of logarithm, (x=e^y), so (f^{-1}(x)=e^x). Step 3: (\ln x) and (e^x) are inverse functions of each other.चरण 1: (y=\ln x) मानें। चरण 2: लघुगणक की परिभाषा से (x=e^y), इसलिए (f^{-1}(x)=e^x)। चरण 3: (\ln x) और (e^x) परस्पर व्युत्क्रम फलन हैं।
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