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MathematicsFunctionsFunctional EquationEasy2 minPYQ_2021

MathematicsEasysingle choice

A function $f (x)$ is given by $f (x) = \frac{5^{x}}{5^{x} + 5}$ , then the sum of the series

$f (\frac{1}{20}) + f (\frac{2}{20}) + f (\frac{3}{20}) + \dots + f (\frac{39}{20})$

is equal to:

Options:

Answer:

C

Solution:

$f (x) = \frac{5^{x}}{5^{x} + 5} and f (2 - x) = \frac{5}{5^{x} + 5}$

$f (x) + f (2 - x) = 1$

$\Rightarrow f (\frac{1}{20}) + f (\frac{2}{20}) + \dots + f (\frac{39}{20})$

$= (f (\frac{1}{20}) + f (\frac{39}{20})) + \dots + (f (\frac{19}{20}) + f (\frac{21}{20})) + f (\frac{20}{20})$

$= 19 + \frac{1}{2} = \frac{39}{2}$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Functional Equation

⏱ 2mℹ️ Source: PYQ_2021

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