2
votes
2answers
38 views

If $ f(x)=x^2-3x+1$ then $ f(x-2) = ?$

If $ f(x)=x^2-3x+1$ then $ f(x-2) = ?$ I'm not sure how to properly deal with this function and solve for $f(x-2)$.
1
vote
1answer
16 views

Intersection of graphs, and no solution for trig functions.

All I know is the c=asin(x-b) I don't know how to check the values of b for 'no solutions,' in the case of trig functions. Can someone people provide an algebraic method to solve this.
0
votes
2answers
50 views

Real Analysis; injective and surjective functions

Let $f$ and $g$ functions from $\mathbb{R}$ to $\mathbb{R}$ given by $$g(x)= x^2-x$$ and $$f(x)= -\sin x$$ i) Is $g$ injective? ii) is $g$ surjective? iii) is $g$ invertible? iv) is $f$ injective? ...
1
vote
2answers
29 views

Proving that function with domain (-1,1) is injective.

Function $g\colon (-1,1) \rightarrow \mathbb R$ is defined by $g(x)=\dfrac{x}{1-x^2}$. Prove that $g(x)$ is injective. Work: I shifted the equation so that it ends up like ...
0
votes
3answers
35 views

inverse of a function f(x)..change x and y

Find the inverse of the function $f(x)= (2x-1)/(x^2-1).$ we switch the x and y letters and then solve the the equation...but it became kind of complicated while solving
1
vote
2answers
57 views

Problem : Solve $|x^2+x-4| =|x^2-4| +|x|$

Problem : Solve $|x^2+x-4| =|x^2-4| +|x|$ We can find the critical point of each modulus function individually then we get : $x =\pm 2;$ and $x = 0$ $x = \frac{-1 \pm \sqrt{17}}{2}$ So there are ...
1
vote
2answers
29 views

Sin & Cos Equation/Relation

If sin(x) = 0.3, find cos(pi-x) how i would solve this: let x = sin-1(0.3) solve for cos(pi-[sin-1(0.3)]) Is there a way to solve this by hand? Is the above method wrong?
2
votes
1answer
58 views

Sketch the Graph. $S(x) = \frac{1}{2} (x-1)^3 +4$

The question is: Sketch the graph of the the function by transforming the graph of an appropriate function of the form $y = x^n$. Indicate all x and y intercepts on the graph. I am really trying to ...
0
votes
0answers
35 views

Question about an exponential funtion

Now we have a function: $f(x)=e^x, x\in \mathbb R$ Question: 1) Assume that $x>0$, discuss the number of the intersects between $f(x)$ and $y=mx^2,m>0$ under different situation. 2)Assume ...
1
vote
1answer
26 views

how to determine a function of a specific shape

I have become very passionate about mathematics lately, but one question is really irritating me, HOW do you determine a function for ANY specific shape ? Is there a certain procedure that enables ...
0
votes
1answer
29 views

Prove this logarithm equation

I keep getting the wrong answer. Can someone please correct my working out a^x=b^(1-x) In(a)^x=In(b)^(1-x) xIn(a)=(1-x)In(b) xIn(a)=In(e)-xIn(b) xIn(a)+xIn(b)=In(e) x[In(a)+In(b)]=Ine ...
0
votes
1answer
39 views

Inverse Function of Logarithm

The answer is A but I don't understand why! $ -2 \log_e (x^2) $ can be re-written as $ -4 \log_e(x) $ right? but why do these two graphs look different? the graph $-2 \log_e (x^2) $ is one to ...
1
vote
2answers
18 views

How to find the Domain for this function

my working out: x+a>0 x>-a x^2-a^2 > 0 x>|a| a^2-x^2>0 |a|>x hmm.. the answer is b ... how, why?
0
votes
1answer
15 views

Maximum value of constant in logarithm problem

The first thing I did was: make: (x-1)^2 - k > 0 (x-1)^2 > k don't know what to do after this point... the maximum value of k is 9 i dont really understand what the maximum value of k is? ...
5
votes
4answers
86 views

Find$f$ s.t. $f(1)=2$, $f(2)= 4$, $f(3)= 6$ and $f(4)= \pi$.

Find a function where $f(1)=2$, $f(2)= 4$, $f(3)= 6$ and $f(4)= \pi$. I got $\dfrac16(x-3)(x-2)(x-1)\pi$ as a start to get rid of $\pi$.
1
vote
2answers
34 views

Describing asymptotic behaviour of a function

For question B! x^2+x+1/x^2 = 1+ [x+1/x^2] shouldnt the answer be asymptote at x=0 and y=1 ?? i dont understand the textbook solution
-1
votes
3answers
36 views

Does the inverse of $g(x)$ exist? If so, what is the inverse, express in interval notation.

Let $g(x)=2+rx-3$ Does the inverse of $g(x)$ exist? Find the inverse of $g(x)$ and express in interval notation.
1
vote
1answer
31 views

How to determine the remaining roots when two distinct real roots and y-intercept are given

A quartic polynomial has 2 distinct real roots at $x=1$ and $x=-3/5$. If the function has a y-intercept at -1 and has $f(2)=2$ and $f(3)=3$, determine the remaining roots and produce an accurate ...
1
vote
1answer
38 views

How does one create a step function?

Is there a general form for the equation of a step function? For example, if I wanted to find the equation of this particular step function: How would I go about doing so? At first I was thinking of ...
-1
votes
2answers
91 views

How can you prove this polynomial is a bijection? [closed]

$ f:\mathbb{R\rightarrow \mathbb{R} }$ $$f(x)=x^7+x^3$$ how can you prove this function is one-to-one and onto? Thanks!
0
votes
3answers
54 views

A difficult equation containing exponent 2 and 3

I couldn't solve this equation: $$ \frac{2}{x^2} + \frac{2}{2x} - \frac{(x+1)^2}{x^3} = \frac{1}{27} $$ Do I have to multiply everything by $x^3$ and also the righthand side $1/27$? $1 \cdot x^3/27 ...
0
votes
1answer
22 views

Floor and Ceiling question

This was a homework question. I wasn't able to get far because I couldn't determine the properties of floor and ceiling functions. Any help would be awesome. $\def\lc{\left\lceil} ...
1
vote
1answer
29 views

Functional equation with $f(1)$ integer

Here is a nice problem: Let $f:R\rightarrow R$ be a function, R is the set of real numbers, satisfying the following properties: $ f(1)$ is an integer and $xf(y)+yf(x)=(f(x+y))^2-f(x^2)-f(y^2)$, for ...
4
votes
2answers
57 views

Functional Equation : If $(x-y)f(x+y) -(x+y)f(x-y) =4xy(x^2-y^2)$ for all x,y find f(x).

Problem : If $(x-y)f(x+y) -(x+y)f(x-y) =4xy(x^2-y^2)$ for all x,y find f(x). My approach : The given equation can be written as $$(x-y)f(x+y) -(x+y)f(x-y) =4xy(x-y)(x+y)$$ $$\Rightarrow ...
1
vote
2answers
47 views

Is a function still a function if it doesn't have any rule?

From what I've read on the internet, I've concluded that function differs from relation in that function can only have one range per domain. So, if for example: ...
1
vote
1answer
48 views

Found an example for solving via quadratic formula in a book where I am wondering if this is correct

As a refresher, I was skimming through a free Calculus online textbook "MOOCULUS massive open online calculus" (https://mooculus.osu.edu/handouts) and stumbled upon the following example solving a ...
3
votes
2answers
53 views

How to prove infinitely many integer values for a square root equation?

I have the equation $y = \sqrt{3x^2 + 1}$, and I need to prove that there will be infinitely many integer solutions. I saw possible solutions with things like Pell's equation, but I did not fully ...
0
votes
1answer
12 views

Re-arrange expression to transformation form

$$\frac{6x-5}{3x+1}$$ How do you write this in the form $$\frac{b}{x+c} + a$$ I know how to find a (2) by asymptote theory, but I don't know how to re-arrange to find B.
1
vote
1answer
51 views

Solution of “quadratic equation” involving functional coefficients.

Suppose I have a "quadratic equation" whose coefficients are functions of the variable to be solved for: $$f(x)x^2+g(x)x+h(x)=0,$$ with $f,g,h\neq 0$. Would it make sense to apply the quadratic ...
0
votes
1answer
58 views

Proving $\left\lfloor n\frac{\log (b)}{\log (a)}\right\rfloor =\left\lfloor \frac{\log \left(b^n+1\right)}{\log (a)}\right\rfloor$

Inspired by this question, I'd like to know how one would go about proving the below more general equation? $$n \in \mathbb{N},\;a \in \mathbb{N},\;b \in \mathbb{N}$$ $$b^n+1 \notin ...
0
votes
1answer
17 views

How can I simplify this rational function for graphing by translation?

I've actually struggled with how to properly simplify this rational function, and I'm hoping someone can point me in the right direction. It's part of my precalculus class/section on graphing rational ...
3
votes
1answer
55 views

Functional inequality and one identity

I'm a high school student from Bonn, Germany and I have to solve the following problem: If $g:R \rightarrow R $ is a function with the property $g(ab)-ag(b)\leq bg(a)$, for all real numbers a and b, ...
1
vote
1answer
54 views

Find $g(x)$ if $f(g(x))=f(x)g(x)$ and $g(2)$=37, $f(x)$ and $g(x)$ are polynomials

Suppose $f(x)$ and $g(x)$ are non-zero polynomials with real coefficients, such that $f(g(x))=f(x)\times g(x)$. If $g(2)=37$, find $g(x)$. I tried plugging $f(x)$ and $g(x)$ as $n$ and $m$ ...
1
vote
3answers
73 views

Domain of an absolute value

How do we solve for a domain of a function, when it involves absolute values? For example (I created the example myself, so it might be a bit weird): $$f(x) = \frac{1}{\sqrt{|2x+1| - |x-3|}}$$ Thank ...
0
votes
3answers
50 views

how can i find the domain of $ f(x)=x^2+1$?

I don't understand how to find the domain ranges of this. I know that it is infinity but why? I know that it cannot equal zero but squaring a zero and adding one makes it 1 so that is a possible ...
0
votes
1answer
17 views

What's mean 'the value $1$ is unchanged under this mapping,find the other value of $x$ which is unchanged'

$$f(x) = \dfrac{4 + x}{2 + 3x}$$ Given that the value $1$ is unchanged under this mapping,find the other value of $x$ which is unchanged.
0
votes
3answers
223 views

$4^x-4^{x-1}=24$ what is the value of $(2x)^x$?"

So, every week our teacher gives us a very difficult question worth 1 point and I can never get them right, so I would highly appreciate the person who tells and explains, in good detail, why this ...
0
votes
0answers
28 views

max min sum product

I am confused with this elementary thing: For all real $x,y$ define $\vee, \wedge$ by $x\vee y=\max\{x,y\}$ and $x\wedge y=\min\{x,y\}$. I am going to know the closed formula of sum and product ...
1
vote
3answers
45 views

Would this proof be considered true.Proving a property of a operation

Ok so the operation [x] is defined to be equal to the integer such that it is $\leq x$ From this definition it holds that : $$ [x] \leq x $$ I need to prove that $$ [x+n] = [x] + n $$ My proof ...
1
vote
2answers
100 views

Inverse of function, containing a fraction

This is basic, I know, but I cannot seem to come up with the right answer. Find the inverse of the function: $$f(x)= \frac3{x+1}$$ My steps: 1. Convert f(x) to y $$y = \frac3{x+1}$$ Switch places ...
1
vote
1answer
34 views

Inverse Function + Reflection In Y-Axis

Not getting any of the answers in MC. Is the answer wrong, or have I done something wrong?
0
votes
1answer
34 views

Find equation of curve based on points

Given a set of points on a curve, how can I use them to find the function of the curve? Then given a point on that curve and the function, how can I find the next point of distance equal to the ...
1
vote
2answers
39 views

Cubic Transformations - Graph shown is best represented by the equation:

The answer is out of B or D: $f(x) = -(x-a)^3 + b$ because turning point at $(0,0)$ is now $(a,b)$ OR $f(x+a)^3$ because "$a$" is implied as negative... $(0,0)$ is now $(-a,b)$ The textbook ...
2
votes
4answers
68 views

How to show an exponential function is symmetric w.r.t. the y-axis.?

The function $\dfrac{1}{2}x + \dfrac{x}{e^x -1}$ is symmetric w.r.t. the y-axis, and I want to demonstrate this. So I basically have to show that $$\dfrac{1}{2}x + \dfrac{x}{e^x -1} = - \dfrac{1}{2}x ...
0
votes
1answer
26 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:
0
votes
2answers
32 views

Finding the Domain of a function

I have to find the domain of these two functions: $$ \sin |x|\quad\text{ and }\quad |\sin x| .$$ I do not really know how to find the domain of these two functions. Any help would be great, I am ...
1
vote
3answers
68 views

The graph of a function $y(x)$ is a straight line in a regular coordinate system if and only if $y(x) = ax + b$?

How does one prove: The graph of a function $y(x)$ is a straight line (no curves) in a regular coordinate system ($x,y$ coordinate system with axis' having interval $c$) if and only if $y(x) = ax + ...
0
votes
3answers
50 views

the simplest function f(1)=-1; f(2)=0; f(3)=1; f(4)=0.

I'm looking for a function that gives f(1)=-1; f(2)=0; f(3)=1; f(4)=0. The other values are undefined and I don't pay any attention on them. The prefered ...
0
votes
2answers
132 views

Even Odd or Neither

If f(x) and g(x) are both even functions, is f + g even? If f(x) and g(x) are both odd functions, is f + g odd? What if f(x) is even and g(x) is odd? Now intuitively I get that for the first one, the ...
0
votes
2answers
20 views

Need help with Function operations

What is the domain of $g(f(x))$ when given $f(x)=2x^{1/2}$ , $g(x) = 9x^2$ and why? It would be appreciated if someone could explain.