## anonymous one year ago Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work. Help please

1. anonymous

@marihelenh can you help me with this one too?

2. anonymous

@freckles

3. marihelenh

You would replace what you have for f(x) into the x position of g(x). $\left( 4x ^{2}+x+1 \right)^{2}-2$ Does that make sense?

4. anonymous

but where does the x^2-2 go

5. anonymous

the -2 is there but the x^2 i only see the ^2 added but not the x

6. marihelenh

The f(x) becomes a function of g(x), so you just replace what f was equal to into wherever the x is in the g equation.

7. anonymous

oh i think i get it

8. anonymous

yes i get it :D

9. marihelenh

Ok great! It is a little difficult trying to explain on here sometimes.

10. anonymous

4x^4+x^3-1 would this be the final answer?

11. anonymous

@marihelenh

12. marihelenh

Just one sec, let me check.

13. marihelenh

No, the answer is actually even longer.

14. marihelenh

To find the answer you would have to do, $(4x ^{2}+x+1)(4x ^{2}+x+1) -2$

15. anonymous

This is so hard, i thought i understood but now i don't.

16. marihelenh

Do you have to simplify it?

17. anonymous

It says Find g(f(x)) so I think I have to but maybe not

18. marihelenh

Well, if you don't have to, you already have your answer, but I will help you simplify it. Just hang in with me. It will seem confusing, but we will get through it and to the answer. OK?

19. anonymous

ok, thank you

20. marihelenh

The first thing you should do, is multiply the first term of the first set by the second set. |dw:1436743172709:dw|

21. anonymous

16x^5?

22. marihelenh

It would be 16x^4 + 4x^3 + 4x^2

23. marihelenh

Then the same thing with the second term |dw:1436743368652:dw| 4x^3 + x^2 + x

24. anonymous

4 times 4 = 16 then 16^4 times x = 16x^5 or the x doesnt add ^1?

25. marihelenh

No, it doesn't. You add the current exponents, so it would be 2 + 2 = 4.

26. anonymous

oh ok

27. marihelenh

Then you would do it with the third term. |dw:1436743540161:dw| 4x^2 + x + 1

28. anonymous

and what happens to the -2?

29. marihelenh

That will get added on in the end when we put all of the terms together.

30. anonymous

so final answer is this 16x^4 + 4x^3 + 4x^2 - 2 ?

31. marihelenh

That is how you multiply the two trinomials out, so then add them all together. $16x ^{4}+4x ^{3}+4x ^{2}+4x ^{3}+x ^{2}+x+4x ^{2}+x+1-2$ (I added in the -2)

32. anonymous

^that last part is so confusing

33. marihelenh

Add like terms $16x ^{4}+8x ^{3}+9x ^{2}+2x-1$

34. marihelenh

Do you understand how I got the three different terms on the pictures by multiplying them out?

35. anonymous

yes that part i understand

36. anonymous

The f(x) becomes a function of g(x) so you just replace what f was equal to into wherever the x is in the g equation. Then you get: (4x^2+x+1)^2(4x^2+x+1)^2-2 then multiply 4x^2 by all terms of second equation to get 16x^4 now multiply x by all terms of second equation to get 4x^3 repeat now with last term to get 4x^2 you get 16x^4 + 4x^3 + 4x^2 now to add the -2 you add like terms to get 16x^4 + 8x^3 + 9x^2 + 2x - 1 would this be good for the answer ?

37. marihelenh

I just put the nine different terms together and then added the -2.

38. marihelenh

Do you just have to explain how to get the answer?

39. anonymous

yes

40. anonymous

41. marihelenh

Ok, well then let me just fix what you have, you were pretty close.

42. anonymous

ok

43. marihelenh

then multiply 4x^2 by all terms of second equation to get 16x^4+4x^3+4x^2 now multiply x by all terms of second equation to get 4x^3+x^2+x repeat now with last term to get 4x^2+x+1 you get 16x^4+4x^3+4x^2+4x^3+x^2+x+4x^2+x+1 now to add the -2 and add like terms to get 16x^4+8x^3+9x^2+2x-1

44. marihelenh

The first three lines were good. You just had to add a little extra into the next ones, but it was all looking good.

45. anonymous

yeah i missed a couple of things, thank you so much for your time :D

46. marihelenh

It's not a problem. I am soooo sorry for how long it took and how confusing it was.

47. anonymous

I don't care as long as I get it, thank you.

48. marihelenh

You're welcome