domain and range Definition and 72 Threads

So it has been a while since I have been in school, but I just picked up one of these elementary calculus books to brush up my basics and I came across this question: The solution the author provided for C(n,r) to be defined was i)n>0 ii) r should be 0<=r<=n iii) n & r should be integers. He...

Problem statement : I copy and paste the problem from the text. You will note that I added the range myself, because it seemed relevant and yet I couldn't do it. Attempt : I could evaluate the domain. The base of the function ##x-4>0\Rightarrow x>4.\hspace{60 pt} (1)## The function...

$$y = f(x) = \sqrt{9-x^2}$$ According to me, Domain: $$ 9-x^2 \geq 0 \implies (x+3)(x-3) \leq 0 \implies x \in [-3,3] $$ which is correct, but this is how I calculate the range: $$y = \sqrt{9-x^2} \implies y^2 = 9-x^2 \implies x^2 = 9-y^2$$ Now, since $$ 9-x^2 \geq 0 $$ we get $$9-9+y^2 \geq 0...

Hi everyone I have the solution to this question, but I'm not sure I understand it. Why is the domain of the composite function and not [0, pi]? Is it because tan^-1 (0 and R+) will always give a value between (-pi/2, pi/2)? I.e. the domain of the composite function refers to x. Is 0...

The domain and range of this function will be the same. We can let ##𝑓(𝑥)=\sqrt{x},𝑥≥0## However, ##𝑦=𝑓(𝑥)≥0##, so the domain and range of ##f## are ##[0,+∞)## And since ##f## is a function, ##f^{-1}s## domain is the range of ##f## and ##f^{-1}s## range is ##f’s## domain. In other words...

Find the inverse function $f^{-1}$ of $f$. Find the range of $f$ and the domain and range of $f^{-1}$ $$f(x)=5 \sin x +2; \quad -\frac{\pi}{2}\le x \le \frac{\pi}{2}$$ exchange x for y and solve for y \begin{align*}\displaystyle x&=5\sin y + 2 \\...

How do you find the domain and range of a graph?

Homework Statement Consider the function ##f\left(x\right)=\sqrt {x+2}##. Determine if the function is a one-to-one function, If so, find ##f^{-1}\left(x\right)## and state the domain and range of ##f\left(x\right)## and ##f^{-1}\left(x\right)## Homework Equations N/A The Attempt at a...

Homework Statement f(x,y) = 1/y^2-x find the domain of f. Given c ∈ R \ {0} find (x, y) ∈ R 2 such that f(x, y) = c. Finally determine the range of f. Homework Equations I know that the domain of the function is anywhere that the function is defined. The Attempt at a Solution in the case of...

Hello, I'm sorry for registering to the the boards and immediately posting a new thread. I did use the search function to try and find a similar thread that addresses the issue I'm having but nothing jumped out at me and frankly I'm so green that I wouldn't know what to look for. This is my...

Homework Statement Suppose f is a function with domain [-2,10] and range [5,10]. Find the domain and range of the following functions. (a) f(2x+4) (b) 2f(x)+4 The Attempt at a Solution [/B] Would I just substitute the in the domain and range values to find the answer?

Homework Statement Find the domain and range of the following function: f(x, y) = ln(x+y) Homework EquationsThe Attempt at a Solution I know that the natural log ln(x) is only defined when x>0, so does that mean that ln(x+y) is only defined when x+y>0? Also, would the range just be all positive...

I need explanation

hey! How do you work out the domain and range of fg(x), do you work out what range of g(x) will fit the domain of f(x)? I have no clue. Thanks

Homework Statement Specify the domain and range of f(x, y) = arccos(y − x2). Indicate whether the domain is (i) open or closed, and (ii) bounded or unbounded. Give a clear reason in each case.Homework EquationsThe Attempt at a Solution y-x2 >= -1 y >= x2 -1 y-x2 <= 1 y <= x2 +1 I sketched it...

I was thinking about a function whose domain and range are absolutely one point , then I'm stuck in finding the domain and range of the following function .. could anyone help $$y=\sqrt{x^2+y^2}$$

I've always been having trouble with the domain and range of inverse trigonometric functions. For example, let's start with an easy one: $\sin^{-1}\left({x}\right)$ Process: First, I draw out the function of $\sin\left({x}\right)$. Then I look at its range and attempt to restrict it so that it...

Homework Statement There are two vertical ovals, one containing the x-coordinate values and one containing the y-coordinate values. The x-axis values: -1, 8, 0 and the y-axis values: -4, 0, -1 (-1,-4) (8,0) and (0,-1) are the three points. Homework Equations I'm not sure this is an equation...

Homework Statement I constructed my own question to try to make sense of the following notation. g(x) = 2√x g : X → Y. What does X and Y equal? Homework Equations For 2√x, x = or > than 0. The Attempt at a Solution g(x) = 2√x g : [0, ∞) → [0, ∞) So X = Y = [0, ∞) The...

Suppose you have a function y = f(x) such that the domain of f(x) is 1 ≤ x ≤ 6 and the range of f(x) is −3 ≤ y ≤ 5. a) Find constants B and C so that the domain of f(B(x − C)) is 8 ≤ x ≤ 9 B= C= b) Find constants A and D so that the range of Af(x) + D is 0 ≤ y ≤ 1 A= D= I'm working on...

Homework Statement What is the domain and range of the function y = \frac{2}{x^2-4} The Attempt at a Solution I'm lost, and I noticed it seems like a difference of squares so what I did is y = \frac{2}{(x-2)(x+2)}. So the x value of vertex is 0. And i subbed this into the equation...

Here is the question: Here is a link to the question: Find the range and domain of function of 2 varibles:? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: Find the domain and range of f(x)= (e^x)/(1+2e^x)? - Yahoo! AnswersI have posted a link there to this topic so the OP can find my response.

Homework Statement Determine the domain and range of the function y=5−e^(−x/2). I am having some trouble with this. Does any have some tips to get started, or a good link to a instructional video? My textbook does not have this section :( Thanks all! Homework Equations The...

Homework Statement If the maximum allowable width, w, of the wall is 100 cm, what are the domain and rand of the function? Remember to include units for both the domain and range. Homework Equations w(d)=2d w(d)=100, so 100=2d, there fore d=100/2 The Attempt at a Solution...

I have a question about domain and range.What are the domain and range of cos(e^{-×}) and \frac{\left|2×-1\right|}{sin(\frac{1}{2}\pi×-\pi)} ?? Thanks..

Homework Statement Find the domain and range of the following function without the use of a calculator: f(x) = sec (pi x/4) Homework Equations As far as I know, this problem doesn't specifically require "equations". Therefore I am leaving this section blank. Not because I am a...

If I am given a function: f(z) = w(x,y) = u(x,y) + iv(x,y) How do I find the domain and range of that function? Are there any good lectures online on this? I know I have to use two planes; One for u and v, and one for x and y. Besides that, I am lost.

I am a bit confused about this matter. While I was studying Calculus I saw an excercise like this: The domain of f(x) [0,2] and the range is [0,1], it also shows its graphic, though it is not important it is something like a parabola, its maximum point is (1,1) and its intersection points are...

Homework Statement Find the domain and range of the function: F(x) = \frac{x}{lxl} Homework Equations ? The Attempt at a Solution domain is all x such that x ≠0 range: do i have to make this into a piecewise function, if so, how?

Homework Statement Eliminate the parameter to find the Cartesian equation of the curve. Problem #1: x = sin t, y = csc t, 0 < t < ∏ / 2 Problem #2: x = sin θ, y = cos 2θ Homework Equations What's shown above is what's listed in the book. However, the authors felt compelled to...

Homework Statement State the domain and range of the function that models each half of the roof (triangle) Homework Equations Y= -0.7x+1.9 (left half) Y= 0.7x+1.9 (right half) The Attempt at a Solution Why is the answer: Left half: domain: −2.7≤x≤0 range: 0≤y≤1.9 Right...

Homework Statement f(x) = (arctan(ln(sqrtx - 1)))^3 Homework Equations domain of arctan: all real numbers range of arctan: -∏/2, ∏/2 The Attempt at a Solution I know that domain is x>0 when x ≠ 1, because I need a positive number to go under the radical and the natural log of 0 is...

Homework Statement The function f has domain (-∞, ∞) and is defined by f(x) = 3e2x. The function g has domain (0, ∞) and is defined by g(x) = ln 4x. (a) Write down the domain and range of f∘g. (b) Solve the equation (f∘g)(x) = 12 2. The attempt at a solution (a) Is it correct...

What are the domain and range of the following: (Note: It is a relation that is not a function.) y^2(x^2 - 1) = x^4

in interval notation? y^2(x^2 - 1) = x^4 (This is my own problem.)

Homework Statement y= -4(√4x-1) -1 in case it's not clear, the 4x-1 part is all under the radical the question is to graph and find the domain and range Homework Equations The Attempt at a Solution This is probably what your supposed to do , but not sure, OK To get the domain set everything...

f(x) = -√(t(1-t)) Domain: 0≤t≥1 (from Null Factor law) Range: 0≤t However, the range was wrong. The answers said that it was -0.5≤t≥0. I have no idea where the -0.5 came from. I substituted the domain values in but i didn't work. It just came out with zero. Can anyone suggest any ideas...

1) Find a continuous function f: (0,1)->R with f[(0,1)]=R I couldn't think of any function except tangent, but its domain is NOT (0,1) though? Any suggestions? 2) Find a continuous function f: (0,1)->R with f[(0,1)]=[0,1] I couldn't think of any function that I know. Any suggestions? 3) Find a...

Homework Statement Find the domain and the range f(x,y)=2x2+3x2+1 Homework Equations non The Attempt at a Solution ... i said that x,y are all real #'s and f(x,y)>=1 or z>=1 is there anything wrong with what i has attempted at? if do could you explain... thanks in advance

Could someone please explain to me what the range and domain of a function is and how to find them? I just don't understand what they mean Thank You

Homework Statement Given f:A→B and g:B→C, let h=g(f(a)) If h is injective, then g is injective. Give a counter example. Homework Equations Injection: Let f:A→B For all f(x1)=f(x2) implies x1=x2 The Attempt at a Solution f(a)=\sqrt{a} from [0, infinity]→[0,infinity]...

So I'm skipping pre-cal with full intentions of picking up on AP Calc. Our summer course work is taken from a book called preparing for calculus. After giving me some who-dad that I knew already everything changed in an instant. There's a little gap that isn't quiet filled. A function is...

In algebra/trig. what kinds of problems have a domain and a range ? Is this true for anything that can be graphed? Because a lot of the time after you finish a problem in precalc. it then asks for the domain or range, so the question becomes, in mathematics, is it possible to find the domain...

Homework Statement Find the range for the function; fg(x) and state its range where f(x)= e^{2x} + 3 and g(x) = ln(x-1) The Attempt at a Solution Putting g into f I reach; fg(x) = e^{2ln(x-1)}+3 (1) - here is where I have the problem, now, I know that it simplifies down to fg(x)...

Homework Statement For the following questions, find the Domain and Range. Use either the graph or turning point method. Homework Equations 1. y= -x+6x-8 2. y= x^2-3x-5 3. y= -x^2+4x+4 And a question on the matter, when you complete the square, as in when I half the middle term...

Find the domain and range of y=sin^2x I have a hard type computing this into my graphing calculator. Can someone help in the steps to find the domain?

Say we have a function, f(x)=x^3 one would say "f is a function from \mathbb{R} to \mathbb{R}" or f: \mathbb{R}\to\mathbb{R} Then say we have a vector function, \vec{g}(t)=<t^2+1,t> . How would one use the above notation? Would it be \vec{g}: \mathbb{R}\to\mathbb{R}^2 ? And...

Homework Statement How do you know whether you restrict the domain or range with a horizontal ellipse ? Homework Equations x^2/49 +y^2/10=1 The Attempt at a Solution

domain and range of the function help needed.. work shown! Given the function f(x)= (3x+4)/(5-2x) find the domain and range of the inverse function of f(x) work shown: it was proven to be one to one since f(x1)= f(x2) found inverse f(x) to be (5x-4)/(3+2x), i believe this is correct...