## anonymous one year ago For f(x)=1/x-5 and g(x)=x^2+2 Find the expression for g(x). Substitute the value of g(x) into the function f(x) in place of x to find the value of f(g(x))

1. Astrophysics

So we're looking for f(g(x))?

2. anonymous

Looking for g(x) too! But not sure if it's just g(x)=x^2+2 orrr

3. Astrophysics

That just means plug in function g(x) where ever there is an x in f(x)

4. Astrophysics

g(x) is just x^2+2

5. Astrophysics

If your f(x) = 1/(x-5) or is it (1/x)-5

6. anonymous

it's 1/(x-5)

7. Astrophysics

Ok, always put brackets! :) So go ahead and find f(g(x)) as I told you how to

8. anonymous

I got 1/(x^2-3)

9. Astrophysics

$f(g(x)) = \frac{ 1 }{ (x^2+2)-5 }$

10. anonymous

It also has a part 2 that says: (gof)(6) a. find f(6) and b Substitute the value you found in Part 1 into g(x) to find g(f(6))

11. Astrophysics

So yes, you're right :)

12. anonymous

thanks!

13. Astrophysics

(g o f)(x) is the same thing as g(f(x))

14. anonymous

oh, so do i just plug in 6 to 1/(x^2-3) ?

15. Astrophysics

So plug in function f(x) in g(x) then plug in 6 for (g o f)(6)

16. Astrophysics

No, that's f(g(x))

17. anonymous

oh so is it 1/(x-5) + 2

18. Astrophysics

$g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2$

19. anonymous

Do i need to simplify that? or no

20. Astrophysics

Just find g(f(6))

21. anonymous

wait, is Find F(6) just plugging in 6 to f(x)

22. anonymous

and g(f(6)) is the equation you gave? for part b

23. Astrophysics

$g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2$ $g(f(6)) = \left( \frac{ 1 }{ 6-5 } \right)^2+2$

24. anonymous

So it's 3 for the question that asks: Substitute the value you found in Part 1 into g(x) to find g(f(6))

25. anonymous

and there's another question that says find f(6) so would that just be 1

26. Astrophysics

Can you post the question, it's a bit confusing with all the notation

27. Astrophysics

Especially when you're not using LaTeX

28. anonymous

1) Find f(6). 2) Substitute the value you found in Part 1 into g(x) to find g(f(6))

29. Astrophysics

I mean take an image of the question

30. Astrophysics

and post it here

31. anonymous

oh sorry! hold on

32. Astrophysics

Yeah, I'm not sure which question is connected to what, so it's a bit confusing :P

33. anonymous

34. anonymous

it was separated into two pages, sorry!

35. Astrophysics

Well I'm not sure why you didn't just take a picture of the full page, but it seems incomplete, your question for part A seems as if it wants you to find a expression using g(x) from the graph.

36. anonymous

Oh, sorry ignore the graph, it's a different question. sorry!!

37. Astrophysics

Huh? Then this really makes no sense, are the pages both completely different questions?

38. anonymous

Nope, they're supposed to go together

39. Astrophysics

Oh I see, the graph is on a different piece of paper!

40. anonymous

yeah!! sorry haha :/

41. Astrophysics

Ok, so lets do it all over again

42. Astrophysics

We're given $f(x) = \frac{ 1 }{ x-5 } ~~~\text{and}~~~~g(x) = x^2+2$ Part 1, A seems they just want you to find the expression for g(x) meaning they are just seeing if you understand the question, so it's just $g(x) = x^2+2$ part B wants you to find the f(g(x)) so we take function g(x) and plug it into f(x) $f(g(x)) = \frac{ 1 }{ (x^2+2)-5 }$

43. Astrophysics

You can do the simplifications, now lets move on to part 2

44. Astrophysics

We need to find f(6) that just means we need to find $f(6) = \frac{ 1 }{ 6-5 }$ which gives us what?

45. anonymous

1!

46. Astrophysics

Good

47. anonymous

and so B would be 3 right?

48. Astrophysics

Lets see

49. Astrophysics

It's asking us to substitute the value we found in part 1, into g(x) so we can find g(f(6))

50. anonymous

yup! so I would just find g(f(x)) right?

51. Astrophysics

What we found in part 1 was $g(x) = x^2+2$

52. Astrophysics

Is the one they are referring to I believe

53. Astrophysics

So all you need to do here is, find g(f(x)) first then g(f(6))

54. Astrophysics

$g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2$

55. anonymous

I got 3

56. Astrophysics

$g(f(6)) = \left( \frac{ 1 }{ 6-5 } \right)^2+2$

57. anonymous

so yes, 3?

58. Astrophysics

Yeah

59. anonymous

Thanks so much for your help!! :))

60. Astrophysics

So what this question is trying to get across is, you knowing what the notation means and what exactly these compositional functions are doing. So notice we actually took what we solved f(6) and just plugged in g(x)

61. anonymous

I get it now haha :) thanks!!

62. Astrophysics

We could've very well put $g(f(6)) = f(6)^2 + 2 = 1^2+2$

63. Astrophysics

Np