







Composition of functions 
20190224 

From Joshua: Let g(x)=(x)^(2)+x1
Find such a function f such that
(fog)(x)=(x)^(4)+2(x)^(3)3(x)^(2)4x+6 Answered by p. 





The domain of f(g(x)) 
20180618 

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





f(x)=x^26x find f(x2) 
20171027 

From Kenneth: f(x)=x^26x find f(x2) Answered by Penny Nom. 





The composition of a function with itself 
20160717 

From Mel: If f(1 + 3x) = 1 * x, solve f(f(x)) Answered by Penny Nom. 





A stone is dropped in a lake 
20150214 

From Wendy:
Hi, I have problems solving this problem. We didn't exactly go over these kind of problems and the book doesn't have an example either. Thank you for your help!
A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 80 cm/s.
(a) Find a function g that models the radius as a function of time t.
g(t) =
(b) Find a function f that models the area of the circle as a function of the radius r.
f(r) =
(c) Find f compose g.
f compose g = Answered by Penny Nom. 





The continuity of f(x,y)=ln(x^2+y^2) 
20130217 

From anu: the question says we have to find the points in the plane where the function is continuous:
f(x,y)=ln(x^2+y^2) . here we aren't given a particular point (x,y) where we have to check a function's
continuity.
what is to be done if we have to check continuity over the whole domain of the function?
please help . Answered by Harley Weston. 





Transposition error 
20121203 

From Carol: What is the correct term for when a child writes 61 instead of 16, or 83 for 38when they switch the place values of a number? Answered by Chris Fisher. 





A function problem 
20121118 

From nahla: f: IN > IN
n > f(n)
for every n that belongs the IN : fof(x) = 4n  3
and for every n that belongs to IN f(2^n) = 2^(n+1) 1
Calculate f(993) Answered by Penny Nom. 





A proof by contraposition 
20121019 

From Rahul: I am not able to understand the following,
To prove that if for all e>0, x0, then x>=e. I understand the approach very well but I do not understand why if x=e then x>=e. If it is so then why not x=
Thanks in advance!'
Rahul. Answered by Penny Nom. 





Composition of functions and one to one 
20121017 

From Ariana: If f o g are one to one function,does it follow that g is one to one? Give reasons for your answers Answered by Penny Nom. 





The position of an aircraft relative to the airport 
20120608 

From Dennis: "Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude, horizontal distance, and bearing. Suppose an aircraft is at altitude 500m, distance 15km, and bearing 35 degrees east of north. What are the x,y, and z components (in meters) of the position vector. The xaxis is east, the yaxis is north and the zaxis is vertical. Answered by Penny Nom. 





Limits and composition 
20111230 

From Rahul: I want to know about limit proofs of composite functions. Like limit of log of a function equals log of limit of the function Answered by Penny Nom. 





The LCM of 6,15 and x is 90 
20111030 

From Richie: Hi there,
There are 2 parts to the question.
#1. Factorise 90. This is easy, 90=2x3x3x5
#2
LCM of 6,15 and x is 90. What are possible values of x if x is odd?
From #1, since 90=6x15, how can this be used to work out possible values of x?
Thanks in advance,
Richie Answered by Penny Nom. 





Composition of functions 
20110905 

From Jenna: Let f(x)=x^21 and g(x)=12x. Find the indicated values.
1. f(g(1)) and g(f(1))
Thanks,
Jenna Answered by Penny Nom. 





Composition of two functions 
20080704 

From Kristian: f(x)= the square of x add to 1 and g(x)=1/x
find: (f o g)x Answered by Penny Nom. 





Composition of functions: feet, inches and yards 
20080405 

From Coya: write a function f(x) that converts feet to inches.Now write a function g(x) that converts yards to feet. Explain what the composite function f(g(x)) means. Then evaluate f(g(x)) for x = 3,6, and 9. Answered by Stephen La Rocque. 





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. 





Transformations and compositions 
20071129 

From mary: Is there any possible relationship between composite functions and the concept of function transformations? Answered by Harley Weston. 





Motion along a line 
20071002 

From Claudette: If the position function of a particle is x(t) = sin^2(2t), find the distance that the particle travels from t = 0 to t = 2 Answered by Harley Weston. 





Derivative of a Function 
20070709 

From Bob: What is the derivative of the function a sub n = [n/(n+1)]^n ? Answered by Stephen La Rocque. 





The composition of functions 
20070614 

From Gilligan: Question from Gilligan, a student:
Let f(x) = x^2, g(x) = 3x and h(x) = (sqrt{x}) + 1. Express each function as a composite of f, g and/or h.
(1) p(x) = 3(sqrt{x}) + 3
(2) Q(x) = (sqrt(sqrt{x}) + 1}) + 1 Answered by Penny Nom. 





Composition functions 
20070612 

From Gilligan: Find functions f and g so that f(g(x)) = H.
(1) H(x) = (1 + x^2)^(3/2)
(2) H(x) = int(x^2 + 1)
I don't know where to start. Answered by Stephen La Rocque. 





Factoring a trinomial 
20070327 

From Kim: Hi, could you please help me solve this.
3x(squared) +20x  7 Answered by Leeanne Boehm. 





solve; 
20061128 

From Monique: solve; f(f(x)) = 2x + 4 ; if f(x) = 1 Answered by Penny Nom. 





Composition of functions 
20061119 

From RJ: Let f0(x) = 2/2x and fn+1 = f0 o fn for n greater than or equal to 0. Find a formula for fn and prove it by mathematical induction. Recall that o represents function composition. i.e., (f o g)(x) = f(g(x)). Answered by Stephen La Rocque. 





Composition of functions 
20061118 

From Oryan: Given f(x)=2x^3 and g(x)4x5, find g(f(1)) Answered by Stephen La Rocque. 





A proof by contraposition 
20060316 

From Eban:
1)by mathematical induction prove that 1^{2} + 3^{2 }+ 5^{2 }+ ...... + (2k1)^{2} = (1/3)k(2k1)(2k+1) for all positive integers k.
2)show that the contrapositive of the following statement is true. if 1 + M^{7} is even, then M is odd.
Answered by Stephen La Rocque. 





fog 
20051112 

From Janice: I am having problem with the (fog) function
(fog) (x). Given f(x)= 2x^{2} ; g(x)= 34x Answered by Penny Nom. 





Limits and composite functions 
20040807 

From Sue: I have two questions, one about a limit and the other about a composite function. If you could help me, I'd really appreciate it.
1. Find the limit:
lim[x>0] (x*csc(x))
I converted csc(x) to cos(x)/sin(x), but I didn't know what to do after that.
2. f(g(x)) = ln(x^2 + 4), f(x) = ln(x^2) and g(x) > 0 for all real x, find g(x):
I'm having trouble with this one because x^2 + 4 isn't a perfect square.
Sue Answered by Penny Nom. 





Making a square 
20030907 

From A student: if I am given any number (say 80 for example), how may I determine the smallest whole number integer which when multipled by it will yield a square number ? In other words if I express this as: 80İ*İnİ=İsquareİnumber, what is the least value of n which will yield a square. 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. 





Composition of functions 
20011216 

From Paula:
 if f(x)= 3x1 and g(x)= 1/2x + 3 find fog(2)
 find the values of x for which tanx=0
Answered by Penny Nom. 





LOG(LN(x)) = 1 
20000728 

From An algebra student: LET F(x)=LOG X AND G(x)= LN X. SOLVE (f *G)(x)= 1 SHOW COMPOSITION AND USE DEFINITION OF LOGS. Answered by Harley Weston. 

