## 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. Please don't just give the answer! Walk me through it. Thank you!

1. Vocaloid

g(f(x)) means take f(x) and substitute it for x in g(x)

2. Vocaloid

g(x) = x^2 - 2 g(f(x)) = f(x)^2 - 2 = (4x^2 + x + 1)^2 - 2 finish by expanding

3. anonymous

actaully it was the other way around... anyhow =)

4. anonymous

i'm confused now. what do you mean the other way around?

5. anonymous

$$\bf f(x) ={\color{brown}{ 4x^2+x+1}}\qquad g(x)={\color{black}{ x^2-2}} \\ \quad \\ g(\ {\color{brown}{ f(x)}}\ )=({\color{brown}{ f(x)}})^2-2$$

6. anonymous

expand as Vocaloid suggested

7. anonymous

okay... so g(f(x)) = (4x^2 + x + 1)^2 - 2. I'm probably way off, but 16x^4 + x^2 + 2 - 2.

8. anonymous

just bear in mind that $$\bf (4x^2 + x + 1)^2 \implies (4x^2 + x + 1)(4x^2 + x + 1)$$

9. anonymous

so was I right? I just had to take away the -2 at the end?

10. anonymous

What are the steps I have to take? Maybe I can figure it out if you tell me the steps to get the answer. Thanks so much for helping me by the way.

11. Vocaloid

not quite (4x^2 + x + 1)^2 = (4x^2 + x + 1)*(4x^2 + x + 1) use foil to expand

12. anonymous

Okay. Foil = First, outer, inner, last?

13. Vocaloid

yes

14. Vocaloid

we also have a middle term in this case, x

15. anonymous

a sec. pls

16. anonymous

so it would be x squared in the middle

17. Vocaloid

|dw:1443485986922:dw|

18. Vocaloid

|dw:1443486003860:dw|

19. Vocaloid

|dw:1443486036186:dw|

20. anonymous

oh! i see now! Gracias!

21. Vocaloid

|dw:1443486079517:dw|

22. Vocaloid

now add everything in black, then subtract 2

23. anonymous

Okay. Un momento por favor! one sec

24. anonymous

$16x ^{4} + 4x^{3} + 4x ^{2} + 4x ^{3} + x ^{2} + x + 4x ^{2} + x + 1$

25. anonymous

$16x ^{4} + 8x ^{3} + 8x ^{3} + x ^{2} +x ^{2} + 1$

26. anonymous

$(16x ^{4} + 16x ^{3} + x ^{4} + 1) - 2$

27. anonymous

@Vocaloid

28. anonymous

I'm probably not doing this right! But am really trying. Thanks for the help!

29. Vocaloid

30. anonymous

what do I do from here?

31. Vocaloid

|dw:1443486993727:dw|

32. Vocaloid

|dw:1443487003487:dw|

33. Vocaloid

|dw:1443487010986:dw|

34. Vocaloid

16x^4 + 4x^3 + 4x^2 + 4x^3 + x^2 + x + 4x^2 + x + 1

35. anonymous

How do I put it all together?

36. Vocaloid

combine like terms

37. anonymous

oh

38. Vocaloid

16x^4 + 4x^3 + 4x^2 + 4x^3 + x^2 + x + 4x^2 + x + 1 = 16x^4 + 8x^3 + 9x^2 + 2x + 1 now subtract 2 = 16x^4 + 8x^3 + 9x^2 + 2x - 1

39. Vocaloid

40. anonymous

how did you get 9x^2?

41. anonymous

oh you added 4x^2, 4x^2, and x^2! Gotcha!

42. anonymous

Wow! Thank you so much for helping me with this problem! You are a great teacher and very patient! Gracias! Muy bien!