Question
Download Solution PDFयदि \(f(x)=\frac{1}{1+x}\), g(x) = f{f(x)} और h(x) = f[f{f(x)}], तो f(x).g(x).h(x) का मान है :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\(f(x)=\frac{1}{1+x}\)
अवधारणा:
दो फलनों की संरचना की अवधारणा का प्रयोग करें।
गणना:
\(f(x)=\frac{1}{1+x}\)
तब
\(g(x)=f(f(x))=\frac{1}{1+f(x)}\)
\(g(x)=\frac{1}{1+\frac{1}{1+x}}\)
\(g(x)=\frac{1+x}{2+x}\)
हमारे पास है \(f(f(x))=\frac{1+x}{2+x}\)
तब
\(h(x)=f(f(f(x)))=\frac{1+f(x)}{2+f(x)}\)
\(h(x)=\frac{1+\frac{1}{1+x}}{2+\frac{1}{1+x}}\)
\(h(x)=\frac{\frac{2+x}{1+x}}{\frac{2x+3}{1+x}}\)
\(h(x)=\frac{2+x}{2x+3}\)
अब,
\(f(x)\cdot g(x)\cdot h(x)=\frac{1}{1+x} \cdot\frac{1+x}{2+x}\cdot\frac{2+x}{2x+3}\)
\(f(x)\cdot g(x)\cdot h(x)=\frac{1}{2x+3}\)
अतः विकल्प (3) सही है।
Last updated on Jul 4, 2025
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