New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Functions question

2022 · 27 Jun · Shift 1 · Q36

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Functions
2022 · 27 Jun · Shift 1 · Q36

Functions question

2022 · 27 Jun · Shift 1 · Q36

JEE MainMathematicsFunctionsNumerical+4 / −1

Let f : R

\to

R be a function defined by

f(x) = {{2{e^{2x}}} \over {{e^{2x}} + e}}

. Then

f\left( {{1 \over {100}}} \right) + f\left( {{2 \over {100}}} \right) + f\left( {{3 \over {100}}} \right) + \,\,\,.....\,\,\, + \,\,\,f\left( {{{99} \over {100}}} \right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Functions

Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : S $\to$ S as $f (n) = {2 n 2 n - 11,, i f n = 1, 2, 3, 4, 5 i f n = 6, 7, 8, 9, 10$ . Let g : S $\to$ S be a…2022 · Numerical
Let $α, β$ and $γ$ be three positive real numbers. Let $f (x) = α x^{5} + β x^{3} + γ x, x \in R$ and $g : R \to R$ be such that $g (f (x)) = x$ for all $x \in R$ . If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ …2022 · MCQ
For $p, q \in R$ , consider the real valued function $f (x) = (x - p)^{2} - q, x \in R$ and $q > 0$ . Let $a_{1}$ , $a_{2^{'}} a_{3}$ and $a_{4}$ …2022 · Numerical
$Let f (x) = a x^{2} + b x + c be such that f (1) = 3, f (- 2) = λ and$ $f (3) = 4$ . If $f (0) + f (1) + f (- 2) + f (3) = 14$ , then $λ$ is equal to :2022 · MCQ
Let a function f : N $\to$ N be defined by $f (n) = 2 n, n - 1, \frac{n + 1}{2}, n = 2, 4, 6, 8, ...... n = 3, 7, 11, 15, ...... n = 1, 5, 9, 13, ......$ then, f is2022 · MCQ
Let S = {1, 2, 3, 4}. Then the number of elements in the set { f : S $\times$ S $\to$ S : f is onto and f (a, b) = f (b, a) $\geq$ a $\forall$ (a, b) $\in$ S $\times$ S } is .2022 · Numerical
Let c, k $\in$ R. If $f (x) = (c + 1) x^{2} + (1 - c^{2}) x + 2 k$ and $f (x + y) = f (x) + f (y) - x y$ , for all x, y $\in$ R, then the value of $∣2 (f (1) + f (2) + f (3) + ...... + f (20)) ∣$ is equal to .2022 · Numerical
Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If $f (g (x)) = 8 x^{2} - 2 x$ and $g (f (x)) = 4 x^{2} + 6 x + 1$ , then the value of $f (2) + g (2)$ is .2022 · Numerical