1
vote
1answer
56 views

Triplets of distinct integers > 1 that return integer values.

If $(A, B, C)$ are distinct integers $> 1$, and $$f(A, B, C) = \frac{\frac{A^2-1}{A} + \frac{B^2-1}{B}}{\frac{C^2-1}{C}},$$ then for what (if any) triplets $(A, B, C)$ is $f(A, B, C)$ an integer? ...
0
votes
0answers
21 views

In need of formula: Gravity at Specific Coordinates [on hold]

Doing Research on the gravitational pull at a specific set of coordinates. Does anyone know how to solve this mathematically? Please Help. Thanks
0
votes
2answers
23 views

Completely factor a polynomial using the rational root theorem and synthetic division

I am currently seriously confused. My problem, as stated above, is about completely factoring a polynomial. My question is, once you get your possible factors, how do you then simplify it down? Ill ...
0
votes
1answer
27 views

Solving Polynomial Equations and Inequalities

The distance, in km, of a ship from its harbour is modeled by the function $d(t)= -3t^3 + 3t^2 + 18t$ where $t$ is the time elapsed in hours since departure from the harbour. a) When does ...
0
votes
4answers
35 views

Can someone walk me through how this expression simplifies to y/x?

I am just wondering how this equation comes to be: it is from an economics problem involving marginal utilities. I have my two variables, $x$ and $y$. Intuitively, how does $$\frac{0.5\times ...
1
vote
1answer
32 views

Find a function where the mode is the minimum

Let $a_i\in\Bbb R$ some collection of data points where $0\le i\le n$. Define the function $$f(x)=\sum_{i=0}^n(x-a_i)^2$$ It is clear that the minimum value of $f$ occurs when $x$ is the mean of ...
0
votes
2answers
22 views

Horizontal Asymptote of Strange Function

What is the horizontal asymptote as x approaches positive infinity of $\sqrt{4x^2 + 5x} - \sqrt{4x^2 + x}$? The horizontal asymptote is in the form $y = k$. Find $k$.
1
vote
2answers
45 views

Difficult algebraic expression for $f(x) = \frac{x-a}{bx-c}$ to find involutory solution

So I read in another thread about involutory functions, he claims for any real numbers $a$ and $b$, the function: $$f(x) = a + \frac{b}{x-a} = \frac{ax + (b-a^2)}{x-a}$$ satisfies $$f(f(x)) = a + ...
1
vote
1answer
30 views

Which has the least value?

Which of the following have the least value if $-1 < x < 0$? (A) $-x$ (B) $1/x$ (C)$-1/x$ (D)$1/x^2 $ (E)$1/x^3$ I'm not sure what to do, but I'll definitely try. We can ...
0
votes
3answers
32 views

Injectivity in function $f(x)=x\cdot|x|+1$

I want to prove that $f(x) = x\cdot|x|+1$ is injective, and if it is; find the inverse of the function. $f(a) = f(b) \iff a|a|+1 = b|b|+1 \iff a|a| = b|b|$ $\begin{cases} -a^2 = b^2 \quad undefined ...
2
votes
2answers
21 views

What conclusion could be drawn about the maps from their compostie?

Let $f \colon A \to B$ and $g \colon B \to C$. Then If $g \circ f$ is injective, then I know that $f$ is injective, but what can we say about the injectivity of $g$? If $g \circ f$ is surjective, ...
1
vote
2answers
29 views

Find the function and domain for $ (f\circ f)$ when $ f(x) = x+ \frac {1} {x} \ $

Find the function and domain for $ (f\circ f)$ My answer is $ \frac {x^4+3x^2+1x} {(x^2+1)(x)}?$ However, the program I am using states I am wrong. What have I done incorrectly?
4
votes
1answer
59 views

Find a function $f(x)$ such that $\forall \epsilon \gt 0, f(x) = f(x + \epsilon)$

Our professor asked us if we can find a function $f(x)$ such that $\forall \epsilon \gt 0, f(x) = f(x + \epsilon)$. In other words, a function that it's periodic no matter how small you pick the ...
1
vote
4answers
30 views

Compose a function based on a word problem

I'm not looking for answers, I'm just having a hard time with composing a function out of a Max/Min problem like this. Possibly just show me how you would compose the function and leave the rest for ...
0
votes
1answer
38 views

Let f : [a,b] ---> R be a differentiable function…

I realize the hint tells me to use the mean value theorem, but I don't quite understand how to begin to relate it to this question? Any help is appreciated. http://i.imgur.com/HiT1QN5.png
0
votes
1answer
30 views

A Question Regarding Remainder Theorem

What is the remainder when $x^3 + 3x^2 - x - 2$ is divided by $(x+3)(x+5)$? You have to solve this using the remainder theorem, which states: If $f(x)$ is divided by $(x-p)$, giving a quotient $g(x)$ ...
0
votes
1answer
31 views

Solving functional equation $f\left(\sum_{i=1}^n a_i^n\right)=\frac{1}{k} \sum_{i=1}^n f(a_i^n).$

Given natural number $n, k$ consider nondecreasing function $f:\mathbb{N}\cup {0} \to \mathbb{N}\cup {0}$ such that $$ f\left(\sum_{i=1}^n a_i^n\right)=\frac{1}{k} \sum_{i=1}^n f(a_i^n), $$ for ...
1
vote
2answers
56 views

Why isn't $f(x)=\sqrt{2-x}$ reflected across the y-axis?

If I try to graph this function, it does not appear to reflect across the y-axis when it comes time to do the reflection. Rather, it is reflected around the point where the function begins on the ...
1
vote
2answers
29 views

Stuck with finding the domain of a function with a logarithm

Find the domain of the function $$g(x)=\log_3(x^2-1)$$ This is what I got so far: $$\{ x\mid x^2-1>0\} =$$ $$\{ x\mid x^2>1\} =$$ $$\{ x\mid x>\sqrt { 1 } \}= $$ I don't know where to ...
0
votes
2answers
57 views

How does one Graph $y= \sin (x/8)$?

I studied trigonometric functions this summer, however, I am lost as to how to apply what I learned to this problem. The question asks me to plot this function. 1) It is a sine function so the ...
0
votes
1answer
29 views

Making a Piecewise Function into a single expression

A phone company gives a 25.00 dollar flat fee up to 200 minutes then .07 dollars for every minute afterwards. Build a function to find the price of any amount of minutes. Not in a piecewise function, ...
0
votes
1answer
29 views

General method for composition of piecewise defined functions

There is a similarity in questions about composition of functions piecewise defined (see e.g. here, here and here). In these questions the goal is always the same: Given $f,g$ piecewise defined, ...
0
votes
1answer
41 views

Decompose to even and odd functions

Suppose we have the function $f(x) = |x-1|$. I have to find the even and odd parts of the function and write them in terms of Heaviside Function. I have no idea what should I do here? I tried and it ...
4
votes
2answers
278 views

I can do the math but not the problems, help? [closed]

So whenever my instructor / teacher is going over the notes and teaching the new lesson to the class, I listen to what he says, take notes, and do the practice problems along with him. Often times I ...
0
votes
3answers
61 views

How do I show algebraically that the period of the tangent function is $\pi$?

How do I show that the positive real number $p$ for which $\tan (x+p)=\tan (x)$ is equal to $\pi$? In essence how do I prove the period of the tangent function is $\pi$? Please bear in mind I am a ...
-1
votes
3answers
67 views

Does f(x) = g(u)?

If $f(x) = x + \sqrt{2-x}$ and $g(u) = u + \sqrt{2-u}$ is it true that $f = g$? I squared both sides $\sqrt{x + \sqrt {2-x}} = \sqrt{u + \sqrt {2-u}}$ $\sqrt{x} + 2-x = \sqrt{u} + 2-u$ I then ...
0
votes
2answers
75 views

Show that $f:\mathbb{R}-\{2\}\to\mathbb{R}-\{5\}$ with $f(x)=\frac{5x-1}{x-2}$ is bijective

Can anyone please help to explain the question and what actually $f: \mathbb{R} - \{2\}$ means ?? I know that bijection means one to one function and onto both. Any idea to start up with this ...
0
votes
1answer
22 views

Finding the vertical shift of a sinusoidal function

I'm currently studying sinusoids, I've been given a graph with a few key points and have been told to find a cosine function which fits it. When it comes to finding the vertical shift of the graph the ...
0
votes
2answers
27 views

Simplify a function with a square root as the numerator

How would I go about simplifying this: $$\frac{\sqrt{x^4 + 3x^2}}{x}$$ thanks!
5
votes
1answer
104 views

At most n functions

Some background: I was trying to solve the functional equation f(f(x))=sin(x). I realized that $f(\pi n)$ is a root of f for all integers n, because $f(f(\pi n))=\sin(\pi n)=0$. Thus, we can write f ...
0
votes
1answer
28 views

Is there a way to do this? Fixed deduction for x rounds where total = fixed amount

I am trying to calculate the reduction amount / step per round for the given: rounds = 1000 points = 80 starting at reward = 1 point So from round 1 which has a reward of 1 point deduct a fixed ...
1
vote
2answers
58 views

How to find the equation of the graph reflected about a line?

Consider the graph of $y = e^x$ (a) Find the equation of the graph that results from reflecting about the line $y = 4$. (b) Find the equation of the graph that results from reflecting ...
0
votes
1answer
22 views

Quadratic Functions: Determine the value of b

I'm having trouble with this question and I'm not sure what to do. Would appreciate any one who helps me out. Question: The point $(-2,1)$ is on the graph of the quadratic function: $f(x) = -x^2 + bx ...
0
votes
1answer
47 views

How to prove: if $x = y$, then $f(x) = f(y)$ (for a function $f$)

The intuition of this for me is that if two elements in the domain are equal, then their images are equal. But I don't know if this is actually true or not, so I want to know if this is for sure. ...
2
votes
2answers
72 views

Why can't equations with unknown inside and outside of a function be solved in a standard way?

For example the equation $$ n2^n = 8 $$ Is true for $n=2$ which can be guessed, but more complicated examples would require some sort of approach. Also with trigonometric functions, $$ x\sin(x) + ...
0
votes
2answers
57 views

Not understanding the answer to the inverse of a function

$$f(x)\quad =1+\sqrt { 1+x } $$ $$y\quad =1+\sqrt { 1+x } $$ $$y^{ 2 }\quad =1+1+x$$ $$y^{ 2 }-2\quad =x$$ How is it $x=y^{ 2 }-2y$ ?
0
votes
2answers
35 views

Finding asymptotes for $f(x)=\frac{x^2+3x-10}{3x^2+13x-10}$

$$f(x)=\frac{x^2+3x-10}{3x^2+13x-10}$$ I know that the horizontal asymptote is $1/3$. To find the vertical asymptotes, I set the denominator equal to zero and used the quadratic formula, and I got ...
0
votes
0answers
11 views

Give the transformations of the following functions.

Give the transformations of the following 3 functions. Can you please give me at least 3 points to plot for each function(keeping the domain restriction in mind)? Also for rational function. Also ...
0
votes
2answers
23 views

Compositions with Restricted Domain.

Hey Guys! How do you do this problem. There is no overlapping domain for f(x) and g(f(x)). Detailed explanation as to how to do the problem will be preferred! Thanks.
1
vote
1answer
29 views

Compositions and Restricted Domains

Hey guys. I got the answer under question 3 (which is circled). Can you please verify if it is correct? If not, can you please specify how to go about this problem? Thanks
0
votes
2answers
49 views

How to find the composition of two functions and its domain?

I have no clue how to go about this problem. A detailed explanation would be preferred. Thanks
0
votes
1answer
58 views

How to find the domains of functions $f(x) = x-5$, $g(x) = \sqrt{x-5}$, and of their sim?

I've been studying on Study Plan Practice, on MyMathLab for my College Algebra class. We're going over the Algebra of Functions right now and several things don't make much sense. The question is: ...
0
votes
1answer
79 views

$f(x+h)$ not equal to $f(x) +f(h)$???

I'm taking College Algebra at a local community college, and I just wasn't able to follow how my professor came to these conclusions. (3 separate times.) $$\frac{f(x+h) - f(x)}{h},$$ $$f(x) = ...
1
vote
1answer
38 views

How many points to span a goniometric wave and how to construct the goniometric function

I have two questions concerning the spanning of a simple trigonometric function: What is the minimum number of points to define/span a "simple" trigonometric wave in two dimensions? Is it possible ...
2
votes
4answers
80 views

Showing Surjectivitity of $f(x) = x^3$

I want to show that the function $f: \mathbb{R} \to \mathbb{R},\; f(x) = x^3$ is surjective. First Question: If a function has an inverse, it is bijective yes? Second Question: Is my process ...
-2
votes
2answers
47 views

Hey guys. Given the graph below, find the equation of the transformed parent function. [closed]

It would be great if there is a detailed explanation. Also, is there a standard method I can use to answer all kinds of graphs including exponents and logs? Thanks
-1
votes
2answers
53 views

Proof of period of $f(ax+b)$

I have been taught that $f(x)$ is called a periodic function with period $T$ if $$f(x)=f(x+T)$$ This I understand completely. Also I have been taught that $$f(ax)=f(ax+T/|a|)$$ if $f(x)$ has a period ...
4
votes
2answers
55 views

Piecewise linear function and absolute value

While writing a solution to homeworks for my students, I had to write the function $$f(x)=\left\{\begin{array}{ll} \frac{x+2}{2}, & x\leqslant -4\\ \frac{x}{4}, & -4\leqslant x\leqslant 4 \\ ...
4
votes
1answer
66 views

Is there an injective function such that $f(x^2)-f^2(x)\ge \frac{1}{4}$?

The exercise asks me this: Is there an injective function such that $f(x^2)-f^2(x)\ge \frac{1}{4}$? ps: $f: \mathbb{R}\to \mathbb{R}$ I really don't know how to start :c, I appreciate hints.
16
votes
3answers
257 views

Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?

My idea is that the two functions are not the same since for the first function, the domain of the function is only non negative reals for the numerator and positive reals for the denominator. ...