# Tagged Questions

36 views

### Find all polynomials p with real coefficients

Find all polynomials $p$ with real coefficients such that $p(x+1)=p(x)+2x+1$. I feel like in this question you let $x+1=x'$.
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### Find all functions that satisfy the following conditions

Find all functions $f:\mathbb Z\to \mathbb Z$ that satisfy the following conditions: (i) $f (0) = 1$ (ii) $f(f (x)) = x$ for all integers x (iii) $f(f(x + 1)+1) = x$ for all integers x How ...
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### If $f:N→N$ such that $f(f(x))=3x$, then find $f(2013)$

If $f:N→N$ such that $f(f(x))=3x$, then what is the value of $f(2013)$?
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### Determining quadratic function of this word problem

I have this word problem in my homework: ...
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### What is the solution of the following functional equation? (I must confess it is a headache for me)

Find all the functions $f: \mathbb{Z} \to \mathbb{Q}$ such that $f(\frac{x+y}{3})=\frac{f(x)+f(y)}{2}$; $\forall x,y\in\mathbb{Z}$ knowing that $\frac{x+y}{3}\in\mathbb{Z}$.
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### Find all continuous functions $f:\mathbb{R} \rightarrow \mathbb{R}$ such that

Find all continuous functions $f:\mathbb{R} \rightarrow \mathbb{R}$ such that $$f(x)^2 - 2\Bigl\lfloor\,2\,\bigl|f(2x)\bigr|\,\Bigr\rfloor f(x) + \Bigl\lfloor{4f(2x)^2-1}\Bigr\rfloor = 0\,.$$ Here ...
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### functional equation, find $h$ continous on $\mathbf{R}$ such that $h(x) + h(2x) + h(4x) = {x^n}$

I am having trouble finding easily $h$ defined and continuous on $\mathbf{R}$ verifying for all $x$ in $\mathbf{R}$, $$h(x) + h(2x) + h(4x) = {x^n}$$ where $n$ is a fixed natural number. I have a ...
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### How to prove that $f(f(x))=-x$ implies that $f$ is not continuous? [duplicate]

I am trying to prove that: Given an $f:\mathbb{R} \rightarrow \mathbb{R}$, if $f(f(x))=-x$ then $f$ is not continuous? any help? Thank you!
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### fabric design using trigonometric functions

is there any trigonometric function or any others that involve trigonometric function, that draw cool fabric shapes or patterns? I have seen some pictures like but with trigonometric functions... ...
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### $g(x+y)=g(x)g(y)$ for all $x,y \in\mathbb{R}$. If $g$ is continuous at $0$, prove that $g$ is continuous on $\mathbb{R}$ [duplicate]

$g(x+y)=g(x)g(y)$ for all $x,y \in\mathbb{R}$. If $g$ is continuous at $0$, prove that $g$ is continuous on $\mathbb{R}$.
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### Finding a function from the given functional equation .

The question asks us to find the function $f(x)$ with the given information Let $f:\mathbb R \rightarrow \mathbb R$ such that $f'(0)=1$ and $f(x+y)=f(x) + f(y) + (e^{x+y})(x+y)-xe^x-ye^y+2xy$ ...
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### Find all polynomials $P(x)$ satisfying this functional equation

Find all polynomials $P(x)$ which have the property $$P[F(x)]=F[P(x)], \quad P(0) = 0$$ where $F(x)$ is a given function with the property $F(x)>x$ for all $x\geq 0$. This is an exercise ...
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### Proving Join Dependencies in MVD

I have a question regarding natural join operations in multivalued dependencies. I know that a join operator joins two tables on similair attributes, however I have a hard time to figure out how to ...
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### Find all functions : $f:\mathbb{R^+}\rightarrow \mathbb{R^+}$ such that:

Find all functions : $f:\mathbb{R^+}\rightarrow \mathbb{R^+}$ such that: $$f(1+xf(y))=yf(x+y)$$ for all $x,y \in \mathbb{R^+}$
### Find all $f:\mathbb{R}^+\to \mathbb{R}^+$ satisfies that:
Find all $f:\mathbb{R}^+\to \mathbb{R}^+$ satisfies that: $$f(x)\cdot f(yf(x))=f(y+f(x))$$ $\forall x,y \in \mathbb{R}^+$