







The domain of f + g 
20191016 

From Angel: The domain of f+g when f(x)=8x+3 and g(x)=15x Answered by Penny Nom. 





The domain of f(g(x)) 
20180618 

From Joshua: What are the restrictions of the domain of f(g(x))? Answered by Penny Nom. 





The inverse of y = x(x  2) 
20161221 

From Sasha: Hello, I recently stumbled upon this question and I haven't been able to figure it out.
Why is the inverse of y=x(x2) not a function?
Suggest a domain restriction which would ensure that the inverse is a function.
Thank You :) Answered by Penny Nom. 





The domain and range of a function 
20160219 

From Genius: State the domain and range
g(x)=x(x1) Answered by Penny Nom. 





The range of a function with a finite domain 
20160125 

From Hannah: Solve y=(1⁄4)x1 if the domain is (4,2,0,2,4).
I don't get how to do this. Can anyone help? Answered by Penny Nom. 





The domain of cos2x/(sinx2) 
20151102 

From Ameen: Find the domain of:
f(x) = cos2x/(sinx2) Answered by Penny Nom. 





A quadratic equation 
20131127 

From corinanna: Hi,
How do you find a quadratic equation given the domain & range,
& or the yintercept? Answered by Penny Nom. 





The domain of a derivative 
20131010 

From Renee: I am looking to find the domain of a derivative of a radical function,
one such as: f(x) = the square root of (8 − x).
I am kind of unclear on how domains work for derivative.
I don't understand how you take a function's domain and use that to
find the derivative's domain.
Thanks! Answered by Penny Nom. 





What is the domain of f(x)=sin(ln(x))/ln(x)? 
20130206 

From Behrooz: Hi, the following problem may be interesting:
What is the domain of f(x)=sin(ln(x))/ln(x)?
Be careful, domain is not obvious.
Best regards
Behrooz Answered by Penny Nom. 





Domain and range 
20120809 

From Lucy: Can two different functions have the same domain and range? Why or why not? Answered by Penny Nom. 





The domain of a function 
20110508 

From Minks: (x^2 + 1 / x^2 +2x  3 ) X ( x^2 9 / x^2  2x  3) Answered by Penny Nom. 





Log[f(x)] 
20100308 

From sourabh: What is the number of solutions of the equation
9 x 2  18 x + 5 = 0 for x, such that the expression
log10[(x+1)(x+2)] exists? Answered by Harley Weston. 





The domain, range and inverse of a relation 
20100108 

From Nazrul: Given that A={2,1,0,1,2}, S={(x,y): x belongs to A, y belongs to A and y^2=x}. How can I find the domain and range of the relation S. What is the inverse relation of S. Please show me the process in details.
Thank you. Answered by Penny Nom. 





y = sin(x) + 3 
20091110 

From Kapilan: When graphing trigonometric functions like SIN and COSINE does f(x)=x
squared equal to SIN or COSINE
Also what is the range, domain, period and ampliltude for y=sin@ + 3 Answered by Harley Weston. 





Domain and range 
20090911 

From Aubrey: I'm supposed to "state the domain/range of each of the following relations" and it's totally not making sense...
Examples:
{(x,y) : x = square root of y}
{(x,y) : y = x + 1, x is some even integer}
Thanks in advance!!
Aubrey Answered by Robert Dawson. 





Range and Domain of a Star 
20090514 

From Larry: I am an old teacher trying to help my grandson. He has to draw a structure to scale and then determine the function, domain and range. One line on the structure is from (0,8) to (8,4). I used the intercept method and found the function to by y=1.5x +8 (I think) but can't find the range and domain) Thanks Answered by Janice Cotcher. 





What is the domain of the function (3x+4)/(x^2+5x+6)? 
20081215 

From Robert: What is the domain of the function (3x+4)/x^2+5x+6 Answered by Harley Weston. 





Quadratic equations arising from practical problems 
20081124 

From Lenval: Why do quadratic equations arising from practical problems often give physically impossible solutions such as negative distances, negative times or, say, a polygon with a negative number of sides? For example: "A river in flood carries a tree tsquared  23t metres downstream in t seconds. How long does it take for the tree to be carried 50 metres downstream?" This gives t=25 and t=2. Please explain the second 'solution', which is not physically possible. Answered by Chris Fisher and Victoria West. 





Domain and range 
20080916 

From Cara: Please help me to find the domain and range of the following function:
F(x)=sin(2x) Answered by Harley Weston. 





What is the domain of (f/g)x? 
20080728 

From Warren: If f(x)=3x5 and g(x) = square root of x5, what is the domain of (f/g)x? Answered by Penny Nom. 





Domain and range 
20080723 

From Cane: Hi, my name is Cane and i am stuck on this problem. Find the doman and
range then graph.
y= square root of(x squared  6x) + Square root of(6x  x squared) Answered by Harley Weston. 





Domain & Range of a Periodic Function 
20080711 

From Michelle: The depth, w metres, of water in a lake can be modelled by the function,
w=5sin(31.5n+63) +12 where n is the number of months since
January 1, 1995. Identify and explain the restrictions on the domain and
range of this function. Answered by Janice Cotcher. 





Domain and range 
20080707 

From marylie: what is the domain and range of f(x)= sq.rootof x ^24??tnx Answered by Harley Weston. 





Two function problems 
20080410 

From keith: find the domain: F(x)= 1/ {ln (x+5)  ln (7x)}
find the inverse: g(t)= sqrt {23 ln (1t)} Answered by Penny Nom. 





Composition of functions 
20080307 

From sharon: Find FoG(x)
F(x)= the square root of x9
G(x)= x^2
and also find GoF and their domains Answered by Penny Nom. 





The range of a function 
20080210 

From Rachel: How do I find the range of this function?
(3x^32x^2+6x7)/(x^23x4) Answered by Harley Weston. 





The domain and range of a function 
20080205 

From Victoria: Please...Please...Please tell me how to find domain and range.
Every text and website i have gone to does not make any sense to me!
Below are two example problems i found on a website...
f(x) = (8x3)/(4x1)
and
y = 2x+1
Please explain step by step how to find the domain and range. Answered by Penny Nom. 





The range of a function 
20071112 

From Camille: Hi There,
I am taking a calculus class by correspondence and part of the introduction is
learning how to find domain and range of functions. I understand how to find the
domain. I also understand that if you find the inverse of the equation and
solve for x to find the domain it will give you the range because the domain
of the inverse is equivalent to the range of the original equation. However when
trying to apply this method to complicated questions (ie: square root in the
denominator) I get confused and can't solve for x.
Camille Answered by Harley Weston. 





Domain and range 
20071012 

From Dawn: Hi, I've been out of school for 8 years and recently picked up a math correspondence course. I'm having trouble trying to figure out the range and domain of a linear function. I've read everything I can find in my text, lessons and on your site and I still can't figure out what I'm suppose to be doing. The function is y=2x+1. Please help. Answered by Penny Nom. 





The domain and range of a quadratic function 
20070717 

From Linda: I have been trying to solve this problem but I'm unable to figure it out. How do I find the domain and range of
y=(x+1)^23? Please explain...thanks! Answered by Stephen La Rocque and Penny Nom. 





Interval of the domain 
20070513 

From Gale: What does the term interval of the domain mean? Answered by Penny Nom and Stephen La Rocque. 





Finding domains using number lines 
20070225 

From Saher: Discuss domain of the function, f(x)= (x+1)(x2) / (x+3), with the entire thing under a square root.
I'm being taught how to find the domain using the number line. Our teacher says that there are 56 choices, but I get stuck somewhere around 2, and I don't know how to give my answers after I've obtained the first one, which seems to be (3, infinity). HELP!! Thank you Answered by Stephen La Rocque. 





Inputoutput table 
20070110 

From Richard: Question is make an input  output table for the function using the domain 0,1,2,3,4, Then state the range of the function.
y =x + 8 ?
y =0.4x +3 ? Answered by Penny Nom. 





The domain of a function 
20061115 

From April: Determine the domain of the function h(x) = 4x/x(x^249) Answered by Stephen La Rocque. 





Domain and range 
20060308 

From Jennifer: How do I find the domain of x2y=1 if the range is {2,0,5,8} Answered by Penny Nom. 





The range of a function 
20050821 

From Kelsey: What is the range of the function f(x) = 4x  6 when the domain is {3,1,1,3,5}? Answered by Penny Nom. 





Domain and range 
20040801 

From JJ: I'm checking domain and ranges of these functions. Are these right? Answered by Penny Nom. 





Domain of a function 
20031014 

From Karim: Find the Domain of the Function H(x) = Log3 (4x + 7)10 H(x) = log base 3 times 4X plus 7 minus 10 i am having problem solving these kinds of problems. Answered by Penny Nom. 





The domain of 1/g(x)  5 
20030703 

From Barbara: If the range of g(x) is ( neg. infinity,4] and the domain of g(x) is ( neg. infinity, infinity), how do I find the domain of 1/g(x)  5? Answered by Penny Nom. 





Domain of a function 
20020720 

From Andy: I'm having difficulty in finding the domain of 1/(x^{2} 2x + 4) one over x squared minus 2 x plus 4. Answered by Penny Nom. 





Functions and relations 
20020425 

From Erin: Here's a few math problems that might drive a person insane ;)  If 2f(x)  3f(1/x) = x^2 what is f(2)?
 What are the domain and range of the following relations?
 x^2  4y^2 = 25
 4x^2 + 9y^2 = 36
 The port of Swan Harbor is 200km away from Merry Town Inlet on a bearing of N50E from Merry Town. A ship leaves Merry Town at 8am and sails N15W at 15 km/h. At the same time, a second ship leaves Swan Harbour on a course of S80W at 20km/hour. How close, to the nearest km, are the two ships at 13:00?
 Prove the identity. 1+sinx + cosx/ 1sinx + cosx = 1+sinx / cosx
Answered by Penny Nom. 





Composition of functions 
20020406 

From Yvonne: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = x^{2}  4 and g(x) = sqrt(x) The range of f(x), x<=4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(x^{2}  4). In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything? Answered by Claude Tardif. 





The domain of a function 
20010408 

From Mina: Let f(x) = (2x^{2}+3x17)/(x+5) What is the domain of f? What are the values of x for which f'(x) does not = 0? Answered by Harley Weston. 





Domain and Range and Zeros 
20010227 

From Beth: 1. f(x)=152xx^{2} 2. g(t)=square root of 4t^{2} 3. y=t3/t^{2}t6 Answered by Penny Nom. 





The domain of the derivative 
20010222 

From Wayne: I know that the domain of f'(x) is a subset of the domain of f(x). Is it necessarily true that the subset will have at most one less element than the domain of the original function? Answered by Harley Wesston. 





Range of a function 
20001121 

From David Bell: Given a rational function such as f(x) = (8x3)/(4x1). How can the range be found. Answered by Penny Nom. 





Domain of a function 
20001115 

From Mickey: state any restrictions on the domain of the function. y = 5x  12 over 27x + 6 x does not equal what________? Answered by Penny Nom. 





An equation involving x to the x 
20000722 

From Joy Peter: I am joy, a teacher teaching Maths at the secondary level and while solving a sum came to this stage when i got x^{x} (1 + log x) = 0, by which we can conclude that x^{x} = 0 or 1 + log x = 0. If x^{x} = 0, than what should be the value of x? I feel that the value of x should then be 0 (zero) but then how do I explain this to the students as we also know that anything to the power of 0 is 1 but here 0 raised to 0 is 1. If this is not defined then how do I explain this? Answered by Penny Nom. 





Domain of a function 
20000119 

From Stacey Hutchison:
What is the domain of: f(x) = 1/(x + 4) Answered by Patrick Maidorn. 





Domain and Range of a Function 
19991114 

From Michelle Mellott: How do you find the range of the following function: 2y^{2}/(y^{2}+5y+6)?? I know the domain is x not equalled to 2, 3. How can one easily find the range? Answered by Harley Weston. 





The Range of a Function. 
19970912 

From Karel Marek: Math Is Book 6 (Ebos/Tuck) question 5(b) gives a surprising answer at the back of the book..The question is: Indicate the domain and range for this: y = sqr(x9) (Square root of) The answer for the domain is x>=9 which is not surprisingly, but the range is y>=0, yER ... which I could understand if you were not allowed to transform the equation into x as the subject.. But all example on the facing page DO TRANSFORM the equation at will with x and/or y as the subject.. Can you explain this... ?? Answered by Chris Fisher. 

