Question

How to solve the functional equation $ f(xf(y)+y^2)-f(xy)=f(2x+y^2)-2$?

score 114 · Answer 1 · 2026-04-15 00:23:27

114

Views

How to solve the functional equation $ f(xf(y)+y^2)-f(xy)=f(2x+y^2)-2$?

Published on 15 Apr 2026 - 0:23

score 103 · Answer 2 · 2026-04-16 16:23:44

103

Views

Find $f: \mathbb R \to \mathbb R$ which satisfies $f\left(xf(y)-y^2\right)=(y+1)f(x-y)$

Published on 16 Apr 2026 - 16:23

score 208 · Answer 3 · 2026-04-16 12:57:48

208

Views

Solving logistic equation $x_{n+1}= \mu x_n ( 1- x_n) $ for $\mu = 2 $ and $\mu = 4$

Published on 16 Apr 2026 - 12:57

score 131 · Answer 4 · 2026-04-15 09:01:03

131

Views

How to find a function $f$ that satisfies the equation $f(x)=af(x-1)+b(f(x-1)^2)$

Published on 15 Apr 2026 - 9:01

score 82 · Answer 5 · 2026-04-17 04:30:13

82

Views

Prove that $f(x)^2+f(x+1)^2 = f(2x+1)$ for the function $f$ satisfying $f(x)=f(x-1)+f(x-2), f(1)=f(2)=1.$

Published on 17 Apr 2026 - 4:30

score 127 · Answer 6 · 2026-04-15 17:16:30

127

Views

Finding all function $f: \mathbb{R} \to \mathbb{R}$ satisfying $f\bigl(f(x)+y+z\bigr)=f(x)+f(y)-f(-z)+f(0)$

Published on 15 Apr 2026 - 17:16

score 76 · Answer 7 · 2026-04-16 22:52:12

76

Views

Find $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying $f(x+y)^2=f(x)^2+yf(x)+xf(y)+y^2$ - Solved.

Published on 16 Apr 2026 - 22:52

score 76 · Answer 8 · 2026-04-17 06:25:13

76

Views

Find all kinds of function $f: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $|x|f(y)+yf(x)=f(xy)+f(x^2)+f(f(y))$

Published on 17 Apr 2026 - 6:25

score 207 · Answer 9 · 2026-04-16 17:23:35

207

Views

Find all the functions $f(x)$ where $f(x\sqrt{2}) = 2f(x)$ and $f(x+1) = f(x)+2x +1$ for all real $x$.

Published on 16 Apr 2026 - 17:23

score 140 · Answer 10 · 2026-04-16 13:10:02

140

Views

Find the function(s) $f:\mathbb{R}\setminus\{0\}\to\mathbb{R}\setminus\{1\}$, $f(xy)=f(x)f(-y)-f(x)+f(y)$, $f(f(x))=\frac1{f\left(\frac1x\right)}$

Published on 16 Apr 2026 - 13:10

score 59 · Answer 11 · 2026-04-17 03:52:59

59

Views

Find all functions $f: \mathbb{R} \to \mathbb{R}$ which satisfies $f(x)-y+f(f(y))=f(x+y)+f(f(x))$.

Published on 17 Apr 2026 - 3:52

score 115 · Answer 12 · 2026-04-16 06:10:31

115

Views

Find the function(s) $f: \mathbb{R} \to \mathbb{R}$ which satisfies $f(x)+f(y)-f(x+y)=f(xy)-f(x)f(y)$.

Published on 16 Apr 2026 - 6:10

score 404 · Answer 13 · 2026-03-26 01:12:41

404

Views

If $f(f(x)) = x+1, f(x+1) = f(x) + 1$, is it true that $f(x) = x + 1/2$?

Published on 26 Mar 2026 - 1:12

score 66 · Answer 14 · 2026-04-16 21:10:11

66

Views

Find all function(s) $f:\mathbb{R} \to \mathbb{R}$ which satisfies $f(x)^2+2xf(y)+y^2=f(x+y)^2$.

Published on 16 Apr 2026 - 21:10

score 147 · Answer 15 · 2026-04-16 07:37:12

147

Views

Find the limit given that $f(1)=1$, $f(x+y)=f(x)+f(y)+2xy$ and $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^4}$

Published on 16 Apr 2026 - 7:37

List Question

How to solve the functional equation $ f(xf(y)+y^2)-f(xy)=f(2x+y^2)-2$?

Find $f: \mathbb R \to \mathbb R$ which satisfies $f\left(xf(y)-y^2\right)=(y+1)f(x-y)$

Solving logistic equation $x_{n+1}= \mu x_n ( 1- x_n) $ for $\mu = 2 $ and $\mu = 4$

How to find a function $f$ that satisfies the equation $f(x)=af(x-1)+b(f(x-1)^2)$

Prove that $f(x)^2+f(x+1)^2 = f(2x+1)$ for the function $f$ satisfying $f(x)=f(x-1)+f(x-2), f(1)=f(2)=1.$

Finding all function $f: \mathbb{R} \to \mathbb{R}$ satisfying $f\bigl(f(x)+y+z\bigr)=f(x)+f(y)-f(-z)+f(0)$

Find $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying $f(x+y)^2=f(x)^2+yf(x)+xf(y)+y^2$ - Solved.

Find all kinds of function $f: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $|x|f(y)+yf(x)=f(xy)+f(x^2)+f(f(y))$

Find all the functions $f(x)$ where $f(x\sqrt{2}) = 2f(x)$ and $f(x+1) = f(x)+2x +1$ for all real $x$.

Find the function(s) $f:\mathbb{R}\setminus\{0\}\to\mathbb{R}\setminus\{1\}$, $f(xy)=f(x)f(-y)-f(x)+f(y)$, $f(f(x))=\frac1{f\left(\frac1x\right)}$

Find all functions $f: \mathbb{R} \to \mathbb{R}$ which satisfies $f(x)-y+f(f(y))=f(x+y)+f(f(x))$.

Find the function(s) $f: \mathbb{R} \to \mathbb{R}$ which satisfies $f(x)+f(y)-f(x+y)=f(xy)-f(x)f(y)$.

If $f(f(x)) = x+1, f(x+1) = f(x) + 1$, is it true that $f(x) = x + 1/2$?

Find all function(s) $f:\mathbb{R} \to \mathbb{R}$ which satisfies $f(x)^2+2xf(y)+y^2=f(x+y)^2$.

Find the limit given that $f(1)=1$, $f(x+y)=f(x)+f(y)+2xy$ and $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^4}$

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