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anonymous
 one year ago
For f(x) = x^2+4 and g(x)=x^22, how would you find (f*g)(x), (g*f)(x), and (f*g)(4)?
https://i.imgur.com/zS0XkTh.png
anonymous
 one year ago
For f(x) = x^2+4 and g(x)=x^22, how would you find (f*g)(x), (g*f)(x), and (f*g)(4)? https://i.imgur.com/zS0XkTh.png

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UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1for (f o g) (x) that means to plug in the g(x) function for every x you find in the f(x) so it should look like \[\large ( f \cdot g)(x) = (x^22)^2+4\] then just expand the left part of the equation you need this part before you can evaluate the result when x = 4 for (g o f ) (x) it means plug in your f(x) equation for all x's inside the g(x) function so we have something like this \[( g \cdot f)(x) = (x^2+4)^22\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So @UsukiDoll, after writing out the first one you can just substitute 4 for X and get something like this? (4^22)^2 +4 which is (162)^2 +4 which becomes (14^2) +4 then then so on, Which gives me 200, so 200 would be the answer for C?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1Your question is asking for parts.. like for part a evaluate when we have (f o g )(x) and then we need that result to answer part c which is evaluate when x=4..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, which is why I substituted 4 as X into the answer to the first one.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1ah. I see.. so we can just leave this unexpanded when x = 4

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[\large ( f \cdot g)(4) = (4^22)^2+4\] \[\large ( f \cdot g)(4) = (162)^2+4\] \[\large ( f \cdot g)(4) = (14)^2+4\] \[\large ( f \cdot g)(4) = 196+4=200\] I got 200 too.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So a is (f⋅g)(x)=(x2−2)2+4, b is (g⋅f)(x)=(x2+4)2−2, and the last is 200. Thanks, this was waaay lass complicated then I thought it would be. I think I got it, lemme know if I'm missing something!

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1I think we need to expand a bit for a and b...

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[( g \cdot f)(x) = (x^2+4)(x^2+4)2\] \[\large ( f \cdot g)(x) = (x^22)(x^22)+4\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1the first outer inner last.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm supposed to simplify final answers, but I guess those aren't final. I know how to foil and distribute, yes.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[( g \cdot f)(x) = (x^2)(x^2)+4(x^2)+4(x^2)+4(4)2\] <

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(x2−2)(x2−2)+4 can simplify to (x^24) x^2+8, right?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1and for the other one \[\large ( f \cdot g)(x) = (x^2)(x^2)+(2x)+(2x)+(2)(2)+4\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1whoa one at a time XD

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[( g \cdot f)(x) = x^4+8(x^2)+162\] when you distributed/used foil/ and simplified you got up until this step right?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[( g \cdot f)(x) = x^4+8(x^2)+14\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1did you get this result for part b when you did foil?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For part b I got to this, so yes! (g . f)(x) = x^4+8(x^2)+14

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1alright so let's get part a \[\large ( f \cdot g)(x) = (x^2)(x^2)+(2x)+(2x)+(2)(2)+4 \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[\large ( f \cdot g)(x) = x^44x^2+4+4\] made a mistake on my latex. CAREFUL!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Simplifying that gives me 2x^2 + 2x^2 8.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[\large ( f \cdot g)(x) = (x^2)(x^2)+(2x^2)+(2x^2)+(2)(2)+4\]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[\large ( f \cdot g)(x) = x^44x^2+4+4 \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[\large ( f \cdot g)(x) = x^44x^2+8\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, I missed the positive 8 and didn't distribute one of the 2 I think. So x^4−4x^2+8 is A.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait a minute, for part b if you substitute 4 now into x^4+8(x^2)+14 I get 398 instead of 200.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1umm for part c you need the result from part a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm an idiot. I get 200.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1a and c are related to each other .... so we obtain the result from part a to answer part c which was 200

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got confused for a second and got mixed up. Oop.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for the help, I think I got it now. :D
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