## anonymous one year ago Find fog and gof and their domains for the pair of functions F(x)=2x^2+3 and g(x)=4x-5 (I have fog, I cannot figure out gof)

1. FibonacciChick666

so first, what is g composed f?

2. FibonacciChick666

the function I mean,

3. anonymous

g should be $2x^2+3$

4. FibonacciChick666

that's what you have for f?

5. anonymous

g(x)=4x-5

6. FibonacciChick666

ok, so I am asking, when you plug f into g, what is the resulting function?

7. FibonacciChick666

ie. $$g(f(x) ~or~ g ~o~ f$$

8. kc_kennylau

Just making things tidier for everyone: $\Large f(x)=2x^2+3$$\Large g(x)=4x-5$$\Large(f\circ g)(x) = 2(4x-5)^2+3$$\Large(g\circ f)(x) = 4(2x^2+3)-5$ (Please correct me if I'm wrong)

9. anonymous

$32x^2-80x+53$

10. anonymous

that was fog

11. anonymous

i dont know what gof is...I need help with that I only know fog, which I just gave an answer of

12. FibonacciChick666

how did you get fog, what did you do? (gof is the same process)

13. FibonacciChick666

or ok, let's say let x=2, what would you do?

14. FibonacciChick666

you'd put a 2 everywhere you see an x right?

15. FibonacciChick666

so in the equation g(x) replace every x with f.

16. FibonacciChick666

then replace every f with what f equals, it's just substitution

17. anonymous

I did $fog=f(4x-5)$ $fog=2(4x-5)^2+3$ which equals $32x^2-80x+53$

18. anonymous

that answer is for fog and now I don't know how to do gof

19. UsukiDoll

for g o f you place your f(x) function into the g(x) function

20. FibonacciChick666

same exact way as above

21. FibonacciChick666

you did it correctly

22. FibonacciChick666

its just g(f) instead of f(g)

23. FibonacciChick666

do you see what I mean?

24. UsukiDoll

some people use different terminology symbols... I don't use that but I do use g o f a lot... read this from right to left... your f(x) function should be placed inside the g(x) function

25. anonymous

I did and it keeps telling me I'm wrong. This is how I would do it... $4(32x^2-80x+53)-5$ which would give me $128x^2-320x+207$

26. FibonacciChick666

ah, you put the wrong function in

27. anonymous

how do I put it in :(

28. FibonacciChick666

29. FibonacciChick666

you plugged f composed with g in instead of just f

30. UsukiDoll

do you see the x in g(x) = 4x- 5 replace that x in g(x) with that entire f(x) function

31. FibonacciChick666

so what is f? Plug that in instead of your answer for part a, then I will double check it.

32. FibonacciChick666

33. anonymous

ok so $g(x)=4(2x^2+3)-5$

34. FibonacciChick666

much better :)

35. UsukiDoll

yes so all you have to do is distribute that 4 for 2x^2+3

36. FibonacciChick666

37. anonymous

final answer should be $8x^2+7$ right?

38. UsukiDoll

we are multiplying

39. FibonacciChick666

well, how do you distribute the 4?

40. UsukiDoll

so what is 4 times 2x^2 and what is 4 times 3

41. FibonacciChick666

so just remember, if you have $a(c+b)=ac+ab$ You have to send the a to b and c

42. anonymous

8x^2+12

43. anonymous

$8x^2+12x-5$

44. FibonacciChick666

ok now that is what happens when you distribute correctly, now, you still had that - five hanging out

45. UsukiDoll

we don't need the x for the 12

46. UsukiDoll

$g(x)=8x^2+12-5$ what is 12 - 5 ?

47. anonymous

so its $8x^2+7$

48. FibonacciChick666

yea

49. FibonacciChick666

You were right to begin with, I apologize

50. FibonacciChick666

I got lost in usuki's comments

51. anonymous

Oh thanks...yeah I was confused that you guys said it was wrong haha

52. FibonacciChick666

yea, I'm sorry about that. I read the we are multip[lying and assumed you added, I didn't notice they come out the same. But anyways, does this make sense now?

53. anonymous

Yeah, is that the final answer?

54. UsukiDoll

yeah

55. FibonacciChick666

well, yes and no

56. UsukiDoll

how is this no?

57. FibonacciChick666

so that is the final answer for what is g composed f, but we are not just loooking for that

58. FibonacciChick666

now, we need to find their domain, for both bantaray

59. anonymous

we are looking for domains

60. FibonacciChick666

now, what does domain mean bant?

61. UsukiDoll

oh geez total miss. . .

62. FibonacciChick666

I got this usuki, you can go

63. anonymous

the domain for fog is $(-\infty,\infty)$

64. FibonacciChick666

h/o I need to find what that was again haha

65. FibonacciChick666

sounds right though

66. FibonacciChick666

yep, that's right

67. FibonacciChick666

now for g?

68. FibonacciChick666

side note, you can also say All real numbers

69. anonymous

Ok, I got the domains now...I figured them out really fast :) I think we are done

70. FibonacciChick666

yep, what did you get for g(f)?

71. anonymous

I have one more question.....Would you mind staying to help me?

72. FibonacciChick666

can you pop open another question and tag me?

73. FibonacciChick666

just close this one to make a new one. It's a bit of a long thread

74. anonymous

yeah sure!