Questions tagged [functions]
For elementary questions about functions, notation, properties, and operations such as function composition. Consider also using the (graphing-functions) tag.
34,017
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Asymptotic roots of equation involving Bessel functions
Let $r_2>r_1>0$, $g\ge 0$, and let $\lambda_n$, $n=1,2,\ldots,\infty$, be the positive roots of
\begin{equation}
J_g(xr_2)Y_g'(xr_1)-J_g'(xr_1)Y_g(xr_2)=0,
\end{equation}
where $J_g'(xr_1)$ is ...
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A function that its integral to infinity is a positive constant and it is negatice at zero [closed]
Having a function $k(x)$ that is related to another function $h(x)$ as
$k(x) = a/h(x)-b$
where $a$ and $b>0$ are constants, is it possible to find a smooth function $h(x)$ so that
$k(x)$ is ...
2
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1
answer
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Finding Quintic Formula using any possible set of functions
Let's say that we are able to create a finite set of functions. The functions can be either single-argument ones (for example Cosine) or two-argument ones (for example Sum). The fuctions can only ...
- 61
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Show $\frac{1}{\ln\left(2\right)}\ln\left(x+1\right)-x^{1+x}<(\arcsin\left(x\right))\cdot\left(1-x\right)$ over $(0,1)$
Problem :
Let $0<x<1$ then we have :
$$\frac{1}{\ln\left(2\right)}\ln\left(x+1\right)-x^{1+x}<(\arcsin\left(x\right))\cdot\left(1-x\right)\tag{I}$$
Some hint :
Making the difference I try to ...
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$g$ is quadratic, and $f(x)=mx + n$ has solutions iff $g(x)=mx + n$ does. Prove that $f=g$. [closed]
I need help with an olympiad function problem. I'm still a beginner so any tips that would help me to come up with ideas would be nice. The problem states :
Let $f:\Bbb R\to\Bbb R$ be an arbitrary ...
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Need help with an equation to get average with minimum value? [closed]
Each person needs to contribute equally as much as they can.
Example, all members need to contribute 25\$ in total, since there are 5 of them, they should give 5\$ each, but some of them have less 5$ ...
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"Finitely distinguishable" family of functions $X \to Y$ [closed]
It's a well-known mathematical puzzle to find an uncountable subset of $\mathcal P(\mathbb N)$ such that any two sets have finite intersection. There's various ways to approach this, such as ...
- 4,762
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What is the limit of this composed trig function (first question)? [duplicate]
This is my first question here so I don't know if I formatted this well. Please let me know how I could improve.
So, I was messing around on desmos, specifically with composing functions n times.
An ...
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Inverse of equal functions
the function $f:\Re \to \Re : f(x)=e^x$ is one-one into and
$g:\Re \to (0,\infty) : g(x)=e^x$ is a one-one onto function
but both functions are same as the functions have the same domain and $f(x)=g(x)...
- 177
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Composition of 2 bijective function is bijective [closed]
Its a theorem that composition of 2 bijective function is bijective but here I have taken an example where composition of 2 bijective function is not bijective. Where am I going wrong ?
$f:${$a,b,c,d$}...
- 177
2
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2
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Why is cubic function one-one? [duplicate]
The cubic function $f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^3$
is to be proven a one-one function which can be proved by this method
if $f(x_1)=f(x_2)$ then,
$x_1^3=x_2^3$
$x_1^3-x_2^3=0$
$(x_1-x_2)(x_1^2+...
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$f(x)$ is a differentiable function satisfying the relation $f(x)=x^2+\int_0^x e^{-t} f(x-t) dt$, then $\sum\limits_{k=1}^9f(k)$ is equal to
$f(x)$ is a differentiable function satisfying the relation $f(x)=x^2+\int_0^x e^{-t} f(x-t) dt$, then $\sum\limits_{k=1}^9f(k)$ is equal to
I first differentiated the given relation on both sides w....
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Confused on Big-O theorem
When in Rosen's Discrete Math Textbook they give the theorem:
Suppose that $f_1(x)$ is $O(g_1(x))$ and that $f_2(x)$ is $O(g_2(x))$.
Then $(f_1 + f_2)(x)$ is $O(g(x))$, where $g(x) = (max(|g_1(x)|,\, ...
- 853
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Co-domain and range of composite functions [duplicate]
if we define a composite function, say fog, between 2 arbitrary functions f and g (assuming that range of g is a subset of domain of f) then can we say that the co domain of fog = co domain of f ? and ...
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When exactly are two functions said to be equal? [duplicate]
One of my books say that two functions (say $f$ and $g$) are equal when they satisfy these two conditions..
$\text{dom}(f)=\text{dom}(g)$
$f(x)=g(x)$ for every $x$ in their common domain.
While the ...
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