Question
Download Solution PDFदिया गया है कि f(x) = \(\log \frac{{{\rm{x}} + 4}}{{{\rm{x}} + 1}}\) और g(x) = \(2{\rm{x}} + {{\rm{x}}^2}\) है, तो f[g(x)] किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
फलन का संयोजन: fog(x) = f(g(x)), इसका अर्थ है कि फलन f(x) के लिए x का मान g(x) है।
उदाहरण: माना कि f(x ) = x + 2 और g(x) = 2x है। तो f(g(x)) = g(x) + 2 = 2x + 2 है।
\(\log {{\bf{a}}^{\bf{n}}} = {\bf{n}}\log {\bf{a}}\)
गणना:
दिया गया है कि, f(x) = \(\log \frac{{{\rm{x}} + 4}}{{{\rm{x}} + 1}}\) और g(x) = \(2{\rm{x}} + {{\rm{x}}^2}\)
f[g(x)] = \(\log \frac{{{\rm{g}}\left( {\rm{x}} \right) + 4}}{{{\rm{g}}\left( {\rm{x}} \right) + 1}}\)
\( = \log \left( {\frac{{2{\rm{x}} + {{\rm{x}}^2} + 4{\rm{\;}}}}{{2{\rm{x}} + {{\rm{x}}^2} + 1}}} \right)\)
अतः विकल्प (4) सही है।
Mistake Pointsविकल्प C के लिए, अंश (4x + x2 + 4) होना चाहिए लेकिन इसे (2x + x2 + 4) के रूप में दिया गया है। इसलिए, विकल्प 4 सही उत्तर है।
Last updated on May 31, 2025
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