JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

A function

f\left( x \right)

is given by

f\left( x \right) = \frac{{{5^x}}}{{{5^x} + 5}}

, then the sum of the series

f\left( {\frac{1}{{20}}} \right) + f\left( {\frac{2}{{20}}} \right) + f\left( {\frac{3}{{20}}} \right) + ... + f\left( {\frac{{39}}{{20}}} \right)

is equal to

View answer and explanation

Correct option: C

\frac{{39}}{2}

Option C (39/2) is correct because by pairing terms of the series using the property f(x) + f(2-x) = 1, the sum simplifies to 39/2.

More Questions from FUNCTIONS

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

f(x)=x(4-x)

f^{-1}(x)

g(f(x))=|\sin x|

f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

S=\left\{x: f(x)=f^{-1}(x)\right\}