All Questions
4
questions
8
votes
3
answers
2k
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Is there a bijective, monotonically increasing, strictly concave function from the reals, to the reals?
I can't come up with a single one.
The range should be the whole of the reals. The best I have is $\log(x)$ but that's only on the positive real line. And there's $f(x) = x$, but this is not strictly ...
- 203
5
votes
2
answers
168
views
Existence of Function Taking Every Value Uncountably Many Times
I am stuck on the following problem coming from a plane geometry theorem I'm working on. This is a generalization of that problem which might actually prove easier to handle. All the techniques that ...
- 233
4
votes
3
answers
1k
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If $a$ and $b$ are roots of $x^4+x^3-1=0$, $ab$ is a root of $x^6+x^4+x^3-x^2-1=0$.
I have to prove that:
If $a$ and $b$ are two roots of $x^4+x^3-1=0$, then $ab$ is a root of $x^6+x^4+x^3-x^2-1=0$.
I tried this :
$a$ and $b$ are root of $x^4+x^3-1=0$ means :
$\begin{cases}
a^4+...
- 217
4
votes
3
answers
5k
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Is $\frac{1}{x}$ a function?
Consider $f(x)=\frac{1}{x}$ defined on set of real numbers.
If every element in domain has image, then above relation is said to be a function.
But for $x=0$, $f(x)=\text{infinity}$.
Does it mean ...
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