## anonymous 5 years ago Maximal domain of g(x)... g(x) = (3) - (4/(x+2)) Is it x + 2 = 0.. x = - 2... Is that how we get the maximal domain??

1. anonymous

The maximal domain is the set of all x that allows your function to exist.

2. anonymous

So here, your function is not defined at the point x=-2 since there, the denominator is 0.

3. anonymous

so it can't equal to zero because it's over something

4. anonymous

oh okay thanks

5. anonymous

So your domain is the set of all x real except for x=0.

6. anonymous

i think real, as long as X not equal to 0

7. anonymous

x+2 not equal to zero

8. anonymous

so is the answer...? R / -2 ?

9. anonymous

yes

10. anonymous

$\mathbb{R} - \left\{ -2 \right\}$

11. anonymous

Thanks :)

12. anonymous

np

13. anonymous

Also what is it's range? + it wants the inverse...

14. anonymous

is the range infinity to 3 ?

15. anonymous

negative infinity?

16. anonymous

u want this (-infinity,2),( 2, infinity)? but i never see a form like that, u just write R-{-2}

17. anonymous

Okay, do you know how to get the inverse?

18. anonymous

You can use the definition for the inverse. g is the inverse of f if $f(g(x))=x=g(f(x))$

19. anonymous

The inverse of your function can be found then as,$f(g(x))=3-\frac{4}{g(x)+2}=x$and solve for g(x).

20. anonymous

do we put the w hole g(x) under that 4 ?

21. anonymous

?

22. anonymous

oh sorry.. do we re arrange the g(x) to the other side or something?

23. anonymous

yeah, you solve for g(x)

24. anonymous

4 = x (g(x)+2)

25. anonymous

where'd you 3 go?

26. anonymous

oh lol, -1 = x (g(x) + 2)

27. anonymous

$3-\frac{4}{g(x)+2}=x \rightarrow g(x)=\frac{4}{3-x}-2$

28. anonymous

check, i'm being distracted by different people

29. anonymous

g(x) = 3- 4/x+2.... and inverse is 3 - 4/g(x) +2... can you just leave it like that?

30. anonymous

y = 3- (4/x+2) x = 3-(4/y+2) and then simplify

31. anonymous

Take your original function. Put g(x) in place of x and replace f(x) with x Solve (rearrange) so you have g(x) = blah blah

32. anonymous

how to simplify after... -1 = x(g(x) + 2) ?

33. anonymous

expand

34. anonymous

x(g(x)+2) = xg(x) + 2x

35. anonymous

subtract 2x from both sides

36. anonymous

divide by x

37. anonymous

but i think you've made a mistake

38. anonymous

I'll write it out

39. anonymous

it wants the inverse g^-1... of g(x) = (3) - (4/(x+2))

40. anonymous

y = 3- (4/x+2) x = 3-(4/y+2) x(y+2) = 3-4 x(y+2)=-1 y+2 = -1/x y = (-1/x) -2 can this make sense?

41. anonymous

Yeah, same thing, different notation.

42. anonymous

yeah it makes sense except the G^-1.... the inverse... it looks different.

43. anonymous

y = g^-1(x)

44. anonymous

I stuffed the g(x) calc. because I'm writing it out on this damn thing, but the procedure is correct

45. anonymous

=) Okay so should I just replace the y's with g(x).. as the answer?

46. anonymous

You should end up with$g^{-1}(x)=2\frac{x-1}{3-x}$

47. anonymous

no no ... don't just replace the y's with g(x)... Do what I said... Take your original function. Put g^-1(x) in place of x and replace f(x) with x Solve (rearrange) so you have g(x) = blah blah

48. anonymous

it looks difficult to do but okay :)

49. anonymous

You know what, there's a lot of confusion here. I'm going to write it out and scan.

50. anonymous

Thanks :D :D :D I'll wait

51. anonymous

Lokisan are you still there?

52. anonymous

yes

53. anonymous

scanning

54. anonymous

Ok alright

55. anonymous

56. anonymous

Ive reformatted my pc so ill down pdf reader now, thanks for the link.

57. anonymous

ok

58. anonymous

Lokisan, did you use the retro version of this site?

59. anonymous

?

60. anonymous

retro

61. anonymous

Yes, there was another version to this site

62. anonymous

That means you joined it after the changes have taken place

63. anonymous

Well, I think the retro was better, as you could type there realtime

64. anonymous

I mean, it was more like a black board, and we didn't have to wait for the whole typing to be over

65. anonymous

oh

66. anonymous

Further more we could erase typed things and we could also type inbetween others' typings

67. anonymous

yeah, this is a pain, and i can't use this site on my phone - not practical

68. anonymous

oh that's heaps better

69. anonymous

Would you mind visiting this one https://docs.google.com/document/d/1-_5IUkf1O4EFkBw-kDEZV1T8THk4lzrpmQEzVKtfHHo/edit?hl=en_GB#

70. anonymous

71. anonymous

Just try it once again or try refreshing it

72. anonymous

That makes sense now! :D Thanks a lot and nice hand writing :)

73. anonymous

No probs

74. anonymous

Fan me!

75. anonymous

Okay, I'm a fan already :)

76. anonymous

Good :)