Question
Download Solution PDFComprehension
निर्देश : निम्नलिखित प्रश्नों के लिए नीचे दिए गए कथनों पर विचार करें:
माना f(t) = \(\rm \ln(t+\sqrt{1+t^2})\) और g(t) = tan(f(t)).
निम्नलिखित कथनों पर विचार करें:
I. f(t) एक विषम फलन है।
II. g(t) एक विषम फलन है।
ऊपर दिए गए कथनों में से कौन सा/से सही है/हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
माना f(t) = \(ln (t+\sqrt{1+t^2}\)
f(-t) = \(ln (\sqrt{1+t^2} -t\)
= \(ln( \frac{1}{t+ \sqrt{1+t^2}})\)
= \(-ln(t+\sqrt{1+t^2})\) = -f(t)
इसलिए, f(t) एक विषम फलन है
अब g(t) = tan f(t)
तब, g(-t) = tan f(-t)
= -tan (f(t)) = -g(t)
इसलिए g(t) भी एक विषम फलन है
अतः, कथन I और II दोनों सही हैं।
इसलिए, विकल्प (c) सही है
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