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monroe17 Group TitleBest ResponseYou've already chosen the best response.2
fog.. when f(x)=x2 g(x)=x^2+3x+4 =((x^2+3x+4)2) = 2x^26x8
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
f(x)=x2 f(g(x))=g(x)2 f(g(x))=x^2+3x+42 f(g(x))=x^2+3x+2
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
You're not multiplying, you're subtracting in this case
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
oh.. so I don't distribute the 2?
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
so for fof.. would is be.. (x2)2=x4?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
no, you're not distributing since it's originally x2 and not 2x
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes, fof is x4
 2 years ago

85295james Group TitleBest ResponseYou've already chosen the best response.0
no the roots is X=1 or 2
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
what about ... (x2)^2+3(x2)+4?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
(x2)^2+3(x2)+4 x^24x+4+3(x2)+4 x^24x+4+3x6+4 x^2x+2
 2 years ago

85295james Group TitleBest ResponseYou've already chosen the best response.0
the polynomial discriminant: =1
 2 years ago

85295james Group TitleBest ResponseYou've already chosen the best response.0
hope that helps
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
how'd you go from (x2)^2+3(x2)+4 to this.. x^24x+4+3(x2)+4 ?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
(x2)^2 (x2)(x2) x(x2)  2(x2) x^2  2x  2x + 4 x^2  4x + 4
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
So (x2)^2 is the same as x^2  4x + 4
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
which makes (x2)^2+3(x2)+4 the same as x^24x+4+3(x2)+4
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
yea, yeah, I wasn't thinking.
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
that's ok
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
I'm gonna try to do this one by myself.. and i'll report back what answer I get lol.. (x^2+3x+4)^2+3(x^2+3x+4)+4...
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
alright
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
is it simplified to.. x^4+3x^2+8+3x^2+9x+12+4? I know that not all the way simplified.. I just wanna know if im sorta on the right track?
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
x^4+3x^2+16+3x^2+9x+12+4..
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
no, you're supposed to have cubed terms in there
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
keep in mind that (x^2+3x+4)^2 (x^2+3x+4)(x^2+3x+4) x^2(x^2+3x+4)+3x(x^2+3x+4)+4(x^2+3x+4)
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
(x^2+3x+4)^2=x^4+6x^3+17x^2+24x+16?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
that is correct, so (x^2+3x+4)^2+3(x^2+3x+4)+4 becomes x^4+6x^3+17x^2+24x+16+3(x^2+3x+4)+4
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
x^4+6x^3+20x^2+33x+24?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
good catch
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
x^4+6x^3+20x^2+33x+32 is the correct final answer
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
my goodness! finally lol! Now, one final question... How do I find the domain of those... :/
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
The domain of any polynomial is the set of all real numbers.
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
since you can plug in any real number into a polynomial function and get a real number out.
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
If f(x) and g(x) are both polynomial functions, then the following are also polynomial functions f(g(x)), g(f(x)), f(f(x)), and g(g(x)) or any combination of composition you can think of are all polynomial functions
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
So the domain of each composite function is the set of all real numbers.
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
Notice nowhere do we have to worry about a) dividing by zero or b) taking the square root of negative numbers. So there are no restrictions on x.
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
so the domain for all four polynomials is (inf,inf)?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
exactly
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
phew.. I thought it was gonna b longer then that. lol! Thank you so much. so for any polynomial.. the domain will be (inf,inf) because there are no restrictions?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
Yes, any number will do for the input of a polynomial. So the domain in interval notation for any polynomial is (inf,inf)
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
You'll only run into domain restrictions if you deal with division of variables or having variables in square roots (or logs)
 2 years ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.2
okay, I gotta remember that :) thank you!
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
you're welcome
 2 years ago
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