# domain

1. ### Math trouble! F(x) problem with a domain twist.

Here is the problem: Let y = f(z) = √(4 − z^2) and z = g(x) = 2x + 3. Compute the compositiony = f(g(x)). Find the largest possible domain of x-values so that the composition y = f(g(x))is defined. The answer: −5/2 ≤ x ≤ −1/2 Can someone guide me through the steps on how to reach such a...
2. ### Composite Function

Hello, I badly need help with a question.. Just to start of by defining the functions. f: Q -> R where f(x) = 0,2cos(pi*x)-7 g: N -> Q where g(x) = 5x/2 h(x) = f(g(x)) therefore h(x)= 0,2cos(5x*pi/2)-7 a) What is the range of h? b) What is the domain of h? c) Is h surjective (onto) ? I...
3. ### Optimization problem - defining domain

Hi, Can someone help me formally define what the domain would be for this question? I was fortunately able to reach the correct solution for this question without a well defined range, but for future sake, I would like to be able to know how to derive it. I know that the domain would...
4. ### Domain and polynomial degree

Hi, I hope someone can help. So I have the following function h(x) = f(x)\cdot (1/f(x)). I'm trying to understand if the degree in the function changes why the domain would be different. For example, let's say that f(x) = (x^2)-25...the domain for h(x) would be all real numbers such that x...
5. ### Finding domain for composite functions

I have f(x)=6/(x-3) g(x)=1/x Find the domains of f(g(x)) and g(f(x)) with steps if possible. Thank you in advance, I really need your help.
6. ### Reciprocal Trigonometric Functions

Hi, I hope someone can help. I'm trying to understand the domain for the reciprocal trigonometric functions. As follows: For secant function: For cosecant function: For cotangent function: // same as secant function's domain I know that the domain must exclude values that make the...
7. ### Determining Domain and Range from y=af[k(x-d)]+c

Hello everyone! This is my first post so if I am breaking any rules or doing something wrong please let me know! I'm doing some review for exams which are coming up soon, and the question I am stuck on is asking for the domain and range of y=-2f(-x+5)+1. Now I assume that first I need to...
8. ### Domain of a Function

How to find the domain of the function. 3/(1 +(4/x^2))^(1/2) when I set the denominator equal to zero, I get stuck 1 + (4/x^2) = 0 x^2 + 4 = 0 x^2 = -4 now cannot take the root of negative
9. ### how to prove domain of polynomial

Hi; How do you go about proving the domain of a polynomial function? I know its domain is (-infinity,infinity) but how do I prove this given a function? Thanks.
10. ### domain of inverse square root

I'm asked to find the domain for this question... My ans is (x-1)^2 + (y+1) ^2 >-1 , but the ans given by the author is different , from the sketch , we can know that the author ans is (x-1)^2 + (y+1) ^2 ≠ -1 , am i right ? Which is correct ? http://imgur.com/a/Kn68f
11. ### domain of function

the domain of this fucntion is given by (x^2) +(y^2) ≤ 16 , but i think it's wrong .... It should be (x^2) +(y^2)< 16 , right ? Since if sqrt (16- (x^2) -(y^2) ) = 0 , the whole equation will become 1/ 0 , which is undefined
12. ### domain of multivariable function

from the graph of x and y shown , we know that the x and y value cant be exceed 3 , since it's a circle , why the domain for x and y is x and y can be any number (R) ?
13. ### Identify the Domain fo the expression

This is one problem I am really stuck on on a quiz I am taking. Identify the Domain of the Expression x+7 _______ X^2 + 8x - 9
14. ### Domain of pdf from cdf

Hello, probably obvious question, but what I would like clarified is, is the the domain of the cdf always the domain of the pdf once you for instance take the derivative of the cdf to find the pdf, the pdf will have the same domain right? Also related question, but if you find a function for a...
15. ### Finding the domain of absolute convergence

Find the domain of absolute convergence for: $$\sum_{n=1}^\infty \frac{(n!)(iz+1)^n} {n^3+ \sqrt {n}}$$ which test should be used in this case? I tried the ratio test, but the terms did not cancel out (some did): \$\lim_{n\to \infty} \frac{(n+1)!(iz+1)^{n+1}} {(n+1)^3 + \sqrt...
16. ### More Domain and Range

Hi! I was just wondering if writing the domain of a circle using interval notation like this: [3,7] was the same as stating it as 3≤x≤7? I was doing a question in my text book and answered all the questions correctly using the method however a box next to the questions said to "Refer to...
17. ### Domain and Range

Hi :) I am just starting to learn about Domain and Range and I'm a bit confused. These questions are giving me a bit of trouble, I'll show you what I'm doing and hopefully you can help me if I'm on the wrong track. {(x,y):x^2+y^2=4, x E [-2,2] } So I know that's the formula for a circle...
18. ### Quadratics Domain and Range?

Question: For the parabola with equation y=x^2+7x+4, find the vertex by completing the square. Hence, find the domain and range. What translation would map the parabola y=x^2 onto y = x^2+7x+4? I understand how to complete the square and I found that the vertex was (-7/2,-33/4) however I don't...
19. ### Finding the domain

I know we have to do U substitution, but i'm not sure how..
20. ### Domain of theta for a polar equation

Hello! I was wondering if there is a way to determine the domain of theta for a polar equation so that the graph creates 1 full rotation back to the origin and no more. For example, if I had the polar equation r=9sin2(theta), I can see that it takes from theta=0 to theta=pi for the graph to go...