A function f ( x ) is given by f(x) = 5 ^ x 5 ^ x + 5 , then the sum of the series f((1)/(20)) + f((2)/(20)) + f((3)/(20)) + + f((39)/(20)) is equal to:

Correct answer: C. (39)/(2) f(x) = 5 ^ x 5 ^ x + 5 and f(2 - x) = 5 5 ^ x + 5 f(x) + f(2 - x) = 1 ⇒ f((1)/(20)) + f((2)/(20)) + + f((39)/(20)) = (f((1)/(20)) + f((39)/(20))) + + (f((19)/(20)) + f((21)/(20))) + f((20)/(20)) = 19 + (1)/(2) = (39)/(2)

JEE Main 202125 FebruaryEvening Shift

Exam: JEE Main
Year: 2021
Date: 25 February
Shift: Evening Shift
Subject: Mathematics
Chapter: Functions

JEE Main 2021 · 25 February · Evening Shift · Mathematics · Functions

A function f ( x ) is given by f(x) = 5 ^ x 5 ^ x + 5 , then the...

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

$f\left(\dfrac{1}{20}\right) + f\left(\dfrac{2}{20}\right) + f\left(\dfrac{3}{20}\right) + \ldots + f\left(\dfrac{39}{20}\right)$

is equal to:

Options

A $\dfrac{19}{2}$
B $\dfrac{49}{2}$
C $\dfrac{39}{2}$
D $\dfrac{29}{2}$

Correct answer

C. $\dfrac{39}{2}$

Step-by-step solution

$f\left(x\right) = \dfrac{{5}^{x}}{{5}^{x} + 5}and f\left(2 - x\right) = \dfrac{5}{{5}^{x} + 5}$

$f\left(x\right) + f\left(2 - x\right) = 1$

$⇒ f\left(\dfrac{1}{20}\right) + f\left(\dfrac{2}{20}\right) + \ldots + f\left(\dfrac{39}{20}\right)$

$= \left(f\left(\dfrac{1}{20}\right) + f\left(\dfrac{39}{20}\right)\right) + \ldots + \left(f\left(\dfrac{19}{20}\right) + f\left(\dfrac{21}{20}\right)\right) + f\left(\dfrac{20}{20}\right)$

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

Practice Functions on Quantrex Academy →

More from Functions

Let ℕ denote the set of all positive integers. Consider the sets A = \ 1, 2, 3, 4, 5\ and… JEE Advanced 2026 Let f:(1,∞)→ℝ be a function defined as f(x) = (x-1)/(x+1) . Let f^ i+1 (x) = f(f^i(x))… JEE Main 2026 Let f be a polynomial function such that _2(f(x)) = ( _2(2+(2)/(3)+(2)/(9)+…∞))·… JEE Main 2026 Let f: ℝ arrow ℝ be defined as f(x) = (2x^2 - 3x + 2)/(3x^2 + x + 3) . Then f is : JEE Main 2026 Let e be the base of natural logarithm and let f: \ 1, 2, 3, 4\ arrow \ 1, e, e^2, e^3\… JEE Main 2026 Let f: R arrow R be a function such that f(x) + 3f((π)/(2) - x) = x , x ∈ R . Let the… JEE Main 2026 The sum of all the integral values of p such that the equation 3 ^2 x + 12 x - 3 = p , x… JEE Main 2026 Let A = \ 1, 2, 3, 4, 5, 6\ . The number of one-one functions f: A arrow A such that f(1)… JEE Main 2026 For the function f:[1,∞) arrow [1,∞) defined by f(x)=(x-1)^4+1 , among the two… JEE Main 2026 Let for some α ∈ ℝ , f:ℝarrowℝ be a function satisfying f(x+y)=f(x)+2y^2+y+α xy for all… JEE Main 2026 Let [·] denote the greatest integer function. If the domain of the function f(x) = ^ -1… JEE Main 2026 The number of functions f: \ 1, 2, 3, 4\ arrow \ a, b, c\ , which are not onto, is: JEE Main 2026 If the domain of the function f(x) = _ (0.6) (|(2x-5)/(x^2-4)|) is (-∞, a] \ b\ [c, d)… JEE Main 2026 Given below are two statements: Statement I: The function f: R arrow R defined by… JEE Main 2026 The sum of all the elements in the range of f(x)=Sgn( x)+Sgn( x)+Sgn( x)+Sgn( x) , x ≠ n… JEE Main 2026 If g(x)=3 x^ 2 +2 x-3, f(0)=-3 and 4 g(f(x))=3 x^ 2 -32 x+72 , then f(g(2)) is equal to: JEE Main 2026 Full Functions list Functions JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs