# Tagged Questions

Elementary questions about functions, notation, properties, and operations such as function composition.

40 views

38 views

### How to antidifferentiate a function not applicable to basic antidifferentiation rules? [closed]

For example, how would one go about finding $\int (\pi(x)) dx$? Is there a certain technique or formula? That is, how does one antidifferentiate a function without using integration rules? How does ...
63 views

### Homeomorphism from $S^1\backslash(0,1)$ to $\mathbb{R}$

I am trying to derive a bijection between $S^1\backslash{(0,1)}$ and the real line, but I am stuck on using the most obvious way Let the top point of the circle be $(0,1)$, and the blue line hits ...
125 views

### How many possible functions?

Take $f:\{1,2,3,4,5,6,7\}$ to $\{0,1,2,3,4\}$ How many such functions satisfy the cardinality of the pre-image of the set $\{3\}$ is equal to $3$. I thought it would be $35$, i.e :$7\choose{3}$ ...
56 views

### Inverse of $f(x) = 2x^2+8x+13?$

How can you find the inverse of $f(x) = 2x^2+8x+13?$ This is what I've tried so far: $y = 2x^2+8x+13$ $x = 2y^2+8y+13$ $x-13 = 2y^2+8y$ $x-13=y(y+8)$ This is where I got stuck. To be clear, I want ...
33 views

### Normal vector on a plot

Do a sketch of $f$ with the equation $f(x,y)=0$. Give in all non singular points of the curve a normal vector. $f(x,y)=x^{3}-x-y$ How can I do this thing with normal vector? I know that singular ...
17 views

### How do I solve this equation $f(x, y) = x - y^3 + y$ local for $h(x)=y$?

How do I solve this equation $f(x, y) = x - y^3 + y$ local for $h(x)=y$? $y^3+y=x$ What next?
20 views

### Calculate Density of Values in Cellular Automata

I am working with a special cellular automata that uses hexagonal cells rather than square cells, a hexagonal grid, rather than a square grid, and the set of complex numbers, rather than a finite set, ...
31 views

### Determine a and b so that function is continious

$$g(t)= \begin{cases} 2t^2 ;& t<-1 \\ at ;&-1<t<1 \\ bt-\frac 12 ;&t>1 \end{cases}$$ How can I determine $a$ and $b$ so this function $g$ is continuous at whole $\mathbb R$. ...
1k views

### A binary operation, closed over the reals, that is associative, but not commutative

I am aware that matrix multiplication as well as function composition is associative, but not commutative, but are there any other binary operations, specifically that are closed over the reals, that ...
74 views

### Domain of the function $\frac{1}{\sqrt {x^{12}-x^9+x^4-x+1}}$

What is the domain of $$\frac{1}{\sqrt {x^{12}-x^9+x^4-x+1}}$$ the answer is $(-\infty,\infty)$. Now the polynomial has degree $12$. Also it's continuously increasing from $1$. So I thought there ...
29 views

### Determining if a function is onto

If our range such as in the question below is all the real numbers excluding $0$, to determine if a function is onto we must ask if all real numbers excluding $0$ can be mapped to at least one value ...
253 views

### The difference between semicontinuity and hemicontinuity.

For a point-to-set function F, is "upper hemicontinuous" the same as "upper semicontinuous"? If not, then what's the difference?
14 views

### Resolution function explicity [on hold]

Examine where the equation $f(x,y)=0$ locally by $y=h(x)$ can be resolved. Calculate in all these places $h'(x)$ by implicit differentiation. Enter the resolution function(s) $h(x)$ explicitly if this ...
91 views

### How many solutions exist for the equation $2\sin(x)+\cos(x)=\sqrt{3}$ in $[0,2\pi]$?

How many solutions exist for the equation $2\sin(x)+\cos(x)=\sqrt{3}$ in $[0,2\pi]$ ? All I could till now : LHS =$2\sin{x}+\cos{x}$ Since, $ā\sqrt{5} \leq 2\sin{x}+\cos{x} \leq \sqrt{5}$ So a ...
A function is defined as $$f(x) = \frac{e^{x^2}-e^{-x^2}}{e^{x^2}+e^{-x^2}}$$ f is from $\mathbb R\to \mathbb R$. check if function is surjective or not, injective nature of function can be proved ...