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If (f:(1,\infty)\to\mathbb{R}), (f(x)=\ln(x-1)), which statement is correct?यदि (f:(1,\infty)\to\mathbb{R}), (f(x)=\ln(x-1)) है, तो सही कथन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is ontoयह आच्छादी है
Step 1: Since (x>1), (x-1>0). Step 2: For any (y\in\mathbb{R}), take (x=1+e^y), then (\ln(x-1)=y). Step 3: A logarithm can give all real values when its inside quantity stays positive.चरण 1: (x>1) होने पर (x-1>0)। चरण 2: किसी भी (y\in\mathbb{R}) के लिए (x=1+e^y) लेने पर (\ln(x-1)=y) मिलता है। चरण 3: अंदर की राशि धनात्मक बनी रहे, तो लघुगणक सभी वास्तविक मान दे सकता है।
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