## anonymous one year ago 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

1. 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 $( g \cdot f)(x) = (x^2+4)^2-2$

2. 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?

3. 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..

4. anonymous

Right, which is why I substituted 4 as X into the answer to the first one.

5. UsukiDoll

ah. I see.. so we can just leave this unexpanded when x = 4

6. 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.

7. 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!

8. UsukiDoll

I think we need to expand a bit for a and b...

9. UsukiDoll

$( g \cdot f)(x) = (x^2+4)(x^2+4)-2$ $\large ( f \cdot g)(x) = (x^2-2)(x^2-2)+4$

10. UsukiDoll

do you know FOIL?

11. UsukiDoll

the first outer inner last.

12. anonymous

I'm supposed to simplify final answers, but I guess those aren't final. I know how to foil and distribute, yes.

13. UsukiDoll

$( g \cdot f)(x) = (x^2)(x^2)+4(x^2)+4(x^2)+4(4)-2$ <-

14. anonymous

(x2−2)(x2−2)+4 can simplify to (x^2-4) x^2+8, right?

15. UsukiDoll

and for the other one $\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x)+(-2x)+(-2)(-2)+4$

16. UsukiDoll

whoa one at a time XD

17. anonymous

okay okay xD

18. 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?

19. UsukiDoll

$( g \cdot f)(x) = x^4+8(x^2)+14$

20. UsukiDoll

did you get this result for part b when you did foil?

21. anonymous

For part b I got to this, so yes! (g . f)(x) = x^4+8(x^2)+14

22. UsukiDoll

alright so let's get part a $\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x)+(-2x)+(-2)(-2)+4$

23. UsukiDoll

$\large ( f \cdot g)(x) = x^4-4x^2+4+4$ made a mistake on my latex. CAREFUL!

24. anonymous

Simplifying that gives me 2x^2 + -2x^2 -8.

25. anonymous

wait oops

26. UsukiDoll

-_- do that again.

27. UsukiDoll

$\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x^2)+(-2x^2)+(-2)(-2)+4$

28. UsukiDoll

$\large ( f \cdot g)(x) = x^4-4x^2+4+4$

29. UsukiDoll

$\large ( f \cdot g)(x) = x^4-4x^2+8$

30. 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.

31. UsukiDoll

yeah

32. 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.

33. UsukiDoll

umm for part c you need the result from part a

34. anonymous

I'm an idiot. I get 200.

35. UsukiDoll

a and c are related to each other .... so we obtain the result from part a to answer part c which was 200

36. anonymous

I got confused for a second and got mixed up. Oop.

37. anonymous

Thanks for the help, I think I got it now. :D