anonymous
  • anonymous
For f(x) = x^2+4 and g(x)=x^2-2, how would you find (f*g)(x), (g*f)(x), and (f*g)(4)? https://i.imgur.com/zS0XkTh.png
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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UsukiDoll
  • UsukiDoll
for (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 \[\large ( f \cdot g)(x) = (x^2-2)^2+4\] 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 \[( g \cdot f)(x) = (x^2+4)^2-2\]
anonymous
  • anonymous
So @UsukiDoll, after writing out the first one you can just substitute 4 for X and get something like this? (4^2-2)^2 +4 which is (16-2)^2 +4 which becomes (14^2) +4 then then so on, Which gives me 200, so 200 would be the answer for C?
UsukiDoll
  • UsukiDoll
Your 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..

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anonymous
  • anonymous
Right, which is why I substituted 4 as X into the answer to the first one.
UsukiDoll
  • UsukiDoll
ah. I see.. so we can just leave this unexpanded when x = 4
UsukiDoll
  • UsukiDoll
\[\large ( f \cdot g)(4) = (4^2-2)^2+4\] \[\large ( f \cdot g)(4) = (16-2)^2+4\] \[\large ( f \cdot g)(4) = (14)^2+4\] \[\large ( f \cdot g)(4) = 196+4=200\] I got 200 too.
anonymous
  • anonymous
So 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
  • UsukiDoll
I think we need to expand a bit for a and b...
UsukiDoll
  • UsukiDoll
\[( g \cdot f)(x) = (x^2+4)(x^2+4)-2\] \[\large ( f \cdot g)(x) = (x^2-2)(x^2-2)+4\]
UsukiDoll
  • UsukiDoll
do you know FOIL?
UsukiDoll
  • UsukiDoll
the first outer inner last.
anonymous
  • anonymous
I'm supposed to simplify final answers, but I guess those aren't final. I know how to foil and distribute, yes.
UsukiDoll
  • UsukiDoll
\[( g \cdot f)(x) = (x^2)(x^2)+4(x^2)+4(x^2)+4(4)-2\] <-
anonymous
  • anonymous
(x2−2)(x2−2)+4 can simplify to (x^2-4) x^2+8, right?
UsukiDoll
  • UsukiDoll
and for the other one \[\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x)+(-2x)+(-2)(-2)+4\]
UsukiDoll
  • UsukiDoll
whoa one at a time XD
anonymous
  • anonymous
okay okay xD
UsukiDoll
  • UsukiDoll
\[( g \cdot f)(x) = x^4+8(x^2)+16-2\] when you distributed/used foil/ and simplified you got up until this step right?
UsukiDoll
  • UsukiDoll
\[( g \cdot f)(x) = x^4+8(x^2)+14\]
UsukiDoll
  • UsukiDoll
did you get this result for part b when you did foil?
anonymous
  • anonymous
For part b I got to this, so yes! (g . f)(x) = x^4+8(x^2)+14
UsukiDoll
  • UsukiDoll
alright so let's get part a \[\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x)+(-2x)+(-2)(-2)+4 \]
UsukiDoll
  • UsukiDoll
\[\large ( f \cdot g)(x) = x^4-4x^2+4+4\] made a mistake on my latex. CAREFUL!
anonymous
  • anonymous
Simplifying that gives me 2x^2 + -2x^2 -8.
anonymous
  • anonymous
wait oops
UsukiDoll
  • UsukiDoll
-_- do that again.
UsukiDoll
  • UsukiDoll
\[\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x^2)+(-2x^2)+(-2)(-2)+4\]
UsukiDoll
  • UsukiDoll
\[\large ( f \cdot g)(x) = x^4-4x^2+4+4 \]
UsukiDoll
  • UsukiDoll
\[\large ( f \cdot g)(x) = x^4-4x^2+8\]
anonymous
  • anonymous
Right, I missed the positive 8 and didn't distribute one of the 2 I think. So x^4−4x^2+8 is A.
UsukiDoll
  • UsukiDoll
yeah
anonymous
  • anonymous
Wait a minute, for part b if you substitute 4 now into x^4+8(x^2)+14 I get 398 instead of 200.
UsukiDoll
  • UsukiDoll
umm for part c you need the result from part a
anonymous
  • anonymous
I'm an idiot. I get 200.
UsukiDoll
  • UsukiDoll
a and c are related to each other .... so we obtain the result from part a to answer part c which was 200
anonymous
  • anonymous
I got confused for a second and got mixed up. Oop.
anonymous
  • anonymous
Thanks for the help, I think I got it now. :D

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