0
votes
1answer
77 views

how to find point where two exponential type functions intersect

I have two functions who intersect each other and i want to find time at which they intersect. The two functions are, $\left(1-\frac{1}{\text{X2}}\right)-\frac{(\text{X1}-1) (\text{X2}-1)}{e^{4 t ...
0
votes
1answer
32 views

Proof of transformations to find an approximate value

I have no idea what this questions is asking, or how to go about solving.. can someone please help? Answer:
1
vote
1answer
32 views

Finding a y(x) that satisfies $ y(x) = \int_0^x \! \left(\frac{t} {y(t)+1}\right)^2 \, \mathrm{d}t $

I'm having problem with finding a y(x) that satisfies $$ y(x) = \int_0^x \! \left(\frac{t} {y(t)+1}\right)^2 \, \mathrm{d}t $$ Here is what I tried to do. $$ y(x) = \int_ \! \left(\frac{x} ...
2
votes
1answer
28 views

Question of how to write certain response

What is the domain of the function $$f(x,y)=\frac{1}{x^2+y^2-1}$$ The answer is clear, right?! $$x^2+y^2-1\neq 0\Longrightarrow x^2+y^2\neq1$$What is the point contained in the circle of ...
1
vote
2answers
99 views

Preimage of a function

The only way to get better at this sort of thing is to practice, and now I'm also trying to ask myself (and try to answer) more conceptual questions. If a circle with radius $r$ is given in ...
0
votes
2answers
54 views

Help with a Function

I'd like some help getting this question on its way, any help would be greatly appreciated. For the following function $$f(x) = \frac1{-(x-5)^2+7}\;,$$ determine: a) The equation of the ...
0
votes
1answer
44 views

About continuous functions and aritmethic progression

I've try solve this question, but I haven't sucess... The problem is the following: A continuous functions $f:[a,b]\rightarrow \mathbb{R}$ assume positive and negative values in its domain, show ...
9
votes
3answers
297 views

Solve the functional equation $f(x)=f\left({x\over 3}\right)+f\left({2x\over 3}\right)$ with $f : [0,\infty) \to \mathbb R$ continuous

Solve the functional equation $$f(x)=f\left({x\over 3}\right)+f\left({2x\over 3}\right)\qquad \forall x\geq 0$$ with $f : [0,\infty) \to \mathbb R$ continuous. I can't manage to get this one ...
-2
votes
2answers
436 views

Change parabolic equation to canonical form

I have equation $y = -x^2 + 2x + 7$. How can I change it to canonical form, which looks like $y^2 = 2px$ ? ($p$ will be parameter) What i ve tried so far: $$\begin{align} y &= -x^2 + 2x + 7\\ y ...
1
vote
1answer
64 views

check for Continuity $x \rightarrow 2x^4-2$

Given the function: $f:\Bbb{R}\rightarrow \Bbb{R},\quad x \rightarrow 2x^4-2$ i am asked to check for Continuity for all values of $x$. i am now overasked how to do this since $\Bbb{R}$ is not a ...
-1
votes
1answer
87 views

simple arithmetic problem but..

i am having problem in this proof. i need to find the certain coefficients of this statement on the right side. given: $P: \mathbb{C} \Longrightarrow \mathbb{C}, \quad P(x) := 12 − 7x + x^2$ $Q : ...
1
vote
3answers
128 views

simple question about min and max functions

i am asked to draw the graph of this min and max functions. these functions are given. $f_1(x) := 2, \quad f_2(x) := 3x, \quad f_3(x) := x^2$ now i need to draw the graph of these functions: ...
1
vote
2answers
170 views

Solve $x^2(1-x) = 1$

I have a problem $x^2(1-x) = 1$ This can be simplified ( I think ) to $-x^3 + x^2 - 1 = 0$ Google shows that there is 1 solution for this in its graph. I am not sure how to get to that solution ...
1
vote
5answers
150 views

Find $x$ such that $\arctan(3/2)+\dots=\arctan x$

Find $x$ such that $$\arctan(3/2) + \arctan(5/4) + \arctan(-5/2) + \arctan(-8/3) = \arctan x.$$
2
votes
3answers
365 views

Maps - question about $f(A \cup B)=f(A) \cup f(B)$ and $ f(A \cap B)=f(A) \cap f(B)$

I am struggling to prove this map statement on sets. The statement is: Let $f:X \rightarrow Y$ be a map. i) $\forall_{A,B \subset X}: f(A \cup B)=f(A) \cup f(B)$ ii) $\forall_{A,B \subset X}: ...
0
votes
1answer
42 views

monotoneness - prove the elementary statement

Let $A, B, C$ be nonempty sets with total order. and let $f\colon A \rightarrow B$ and $g\colon B \rightarrow C$ be maps. Prove these statements: a) If $f, g$ are antitone, then $g \circ f$ is ...
0
votes
2answers
238 views

Counting functions

How many functions are possible from the set $A=\{0,1,2\}$ into the set $B =\{0,1,2,3,4,5,6,7\}$ such that $f(i) \le f(j)$ for $i \lt j$ and $i,j \in A$? I am not sure which counting model ...
0
votes
1answer
30 views

Trouble on writing the function for an account record pagination problem

I have this problem about account record pagination. I have to write the function that describes the total pages needed to contain those account records. This is the problem: ...