La matemática es una ciencia exacta, pero en ocasiones la forma de solucionar problemas en…
Student I’m working on composite functions, but do not understand what the «domain» is or how to find it. I can work through the problem, but am lost when it comes to the domain. Please help!
(Tutor) Hi, my name is Juan. How are you today?
Student I’m well. How are you?
(Tutor) I’m good :D, ok let’s get started!
Student ok. I’m needing to understand, what the «domain» is and how to find it?
the domain is all the values that «x» can take
let’s find the domain of f(x)
in that case does x have any restriction?
I mean is there an x value that we can’t use?
Student no. I don’t think so
so the domain of that function is all real numbers
is there an x value that we can’t use?
(Tutor) You got it!
(Tutor) so the domain of this function is
all real numbers except zero
is it more clear?
should I try to explain it in a different way?
Student yes.. domain is all values that x can be for the given function
(Tutor) correct! :D
(Tutor) let’s go back to the problem
(Tutor) in this case
the domain of f(x) is all real numbers
how about g(x)?
Student I think i’m still slightly confused.
(Tutor) in that function
is there any x value that we can’t use?
Student no, i don’t think so
(Tutor) so the domain is all real numbers
(Tutor) Clue: the domain of a polynomial is always all real numbers
f(x) and g(x) are polynomials
Student ok. i see
(Tutor) so the domain will be all real numbers
and how about (fog)(x)
(Tutor) correct :D
but they are asking for gof
(Tutor) ok do you know how to find it?
we have to use g
how would it be?
do you need help?
Student i think i’ve got it. I had trouble with the buttons
what are you trying to do?
Student 2(4x +1)squared + 5(4x+1)
Student 2(16x 2 + 8x + 1) + 20x + 5
32x 2 + 16x + 2 + 20 + 5
(Tutor) it is 20x
but well done!
Student equals 32x 2 + 36x +7
You got it!
And what’s the domain of that function?
I understand what you wrote
but it should be written
Student right, negative on the left
Student Thank you so much for your help! :)
(Tutor) No problem! It was great to work with you!
Student thanks. Bye
Colaborador: Juan Cruz, Tutor Colombiano de Álgebra