Question

Basic functional equation: $ f ( x y ) = f ( x ) + f ( y ) $

score 43 · Answer 1 · 2018-05-05 11:56:26

43

Views

Basic functional equation: $ f ( x y ) = f ( x ) + f ( y ) $

Published on 05 May 2018 - 11:56

score 86 · Answer 2 · 2018-05-05 13:56:55

86

Views

$f(x)$ such that $f(x)*f(f(x)+\frac{1}{x})=1$ and $f(x) > - \frac{1}{x}$ $ \forall$ $ x > 0$ and $f(x)$ is an injective function

Published on 05 May 2018 - 13:56

score 312 · Answer 3 · 2018-05-06 02:39:04

312

Views

Decide whether or not there exists $f(f(x))=5x-\lfloor 5x\rfloor$

Published on 06 May 2018 - 2:39

score 82 · Answer 4 · 2018-05-07 14:24:00

82

Views

Find a if $\sum_{K=1}^n f(a+K)=2n(33+n)$

Published on 07 May 2018 - 14:24

score 59 · Answer 5 · 2018-05-08 16:13:55

59

Views

$f(s,u) + f(u,t) = f(s,t)$ implies $f(s,t) = g(t)- g(s)$

Published on 08 May 2018 - 16:13

score 93 · Answer 6 · 2018-05-10 21:01:11

93

Views

$f(a+b) = f(a) \cdot f(b)$

Published on 10 May 2018 - 21:01

score 237 · Answer 7 · 2018-05-11 07:13:13

237

Views

A functional equation problem: $ \frac { f \left( f ( y ) ^ 2 + x y \right) } { f ( y ) } = f ( x ) + y $

Published on 11 May 2018 - 7:13

score 136 · Answer 8 · 2018-05-12 14:40:46

136

Views

Functional equation $f(x)+f(y)-f(x+y)=4f\left(\frac{x}{2}\right)f\left(\frac{y}{2}\right)f\left(\frac{x+y}{2}\right)$

Published on 12 May 2018 - 14:40

score 4.5k · Answer 9 · 2018-05-13 15:22:36

4.5k

Views

For which of the following functions is $f(a+b) = f(a) + f(b)$?

Published on 13 May 2018 - 15:22

score 175 · Answer 10 · 2018-05-14 20:02:20

175

Views

Function Equation Question Involving $f(xy)=f(x)f(y)-f(x+y)+1$

Published on 14 May 2018 - 20:02

score 106 · Answer 11 · 2018-05-14 23:31:11

106

Views

Function $f:\mathbb{R}\mapsto \mathbb{R}$ satisfying $f(f(x))=x+\lfloor x\rfloor$

Published on 14 May 2018 - 23:31

score 28 · Answer 12 · 2018-05-15 01:25:00

28

Views

Solutions to Functional Equation

Published on 15 May 2018 - 1:25

score 113 · Answer 13 · 2018-05-15 04:44:26

113

Views

Functional equation: $f(x^2+f(y))=y+f^2(x)$.

Published on 15 May 2018 - 4:44

score 89 · Answer 14 · 2018-05-15 09:20:14

89

Views

Proving that a functional equation is constant

Published on 15 May 2018 - 9:20

score 1k · Answer 15 · 2018-05-15 23:14:19

1k

Views

Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

Published on 15 May 2018 - 23:14

List Question

Basic functional equation: $ f ( x y ) = f ( x ) + f ( y ) $

$f(x)$ such that $f(x)*f(f(x)+\frac{1}{x})=1$ and $f(x) > - \frac{1}{x}$ $ \forall$ $ x > 0$ and $f(x)$ is an injective function

Decide whether or not there exists $f(f(x))=5x-\lfloor 5x\rfloor$

Find a if $\sum_{K=1}^n f(a+K)=2n(33+n)$

$f(s,u) + f(u,t) = f(s,t)$ implies $f(s,t) = g(t)- g(s)$

$f(a+b) = f(a) \cdot f(b)$

A functional equation problem: $ \frac { f \left( f ( y ) ^ 2 + x y \right) } { f ( y ) } = f ( x ) + y $

Functional equation $f(x)+f(y)-f(x+y)=4f\left(\frac{x}{2}\right)f\left(\frac{y}{2}\right)f\left(\frac{x+y}{2}\right)$

For which of the following functions is $f(a+b) = f(a) + f(b)$?

Function Equation Question Involving $f(xy)=f(x)f(y)-f(x+y)+1$

Function $f:\mathbb{R}\mapsto \mathbb{R}$ satisfying $f(f(x))=x+\lfloor x\rfloor$

Solutions to Functional Equation

Functional equation: $f(x^2+f(y))=y+f^2(x)$.

Proving that a functional equation is constant

Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

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