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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

$If (x + y) = f (x) f (y) and \sum_{x = 1}^{\infty} f (x) = 2, x, y \in N is the set of all natural numbers, then the value of \frac{f (4)}{f (2)} is :$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{9}$

$\frac{4}{9}$

$\frac{4}{9}$

$Let f (x) = a^{x} \sum_{x = 1}^{\infty} f (x) = 2 \Rightarrow a + a^{2} + a^{3} . . . \infty terms = 2 \Rightarrow \frac{a}{1 - a} = 2 \Rightarrow a = \frac{2}{3} \Rightarrow f (x) = {(\frac{2}{3})}^{x} Now, \frac{f (4)}{f (2)} = \frac{{(\frac{2}{3})}^{4}}{{(\frac{2}{3})}^{2}} = \frac{4}{9}$

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$If (x + y) = f (x) f (y) and \sum_{x = 1}^{\infty} f (x) = 2, x, y \in N is the set of all natural numbers, then the value of \frac{f (4)}{f (2)} is :$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{9}$

$\frac{4}{9}$

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Previous Year Papers

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If x + y = fxfy and ∑x = 1∞ fx = 2, x, y ∈ N is the set of all natural numbers, then the value of f4f2 is : 23 13 19 49

$If (x + y) = f (x) f (y) and \sum_{x = 1}^{\infty} f (x) = 2, x, y \in N is the set of all natural numbers, then the value of \frac{f (4)}{f (2)} is :$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{9}$

$\frac{4}{9}$