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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))

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  1. Astrophysics
    • one year ago
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    So we're looking for f(g(x))?

  2. anonymous
    • one year ago
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    Looking for g(x) too! But not sure if it's just g(x)=x^2+2 orrr

  3. Astrophysics
    • one year ago
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    That just means plug in function g(x) where ever there is an x in f(x)

  4. Astrophysics
    • one year ago
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    g(x) is just x^2+2

  5. Astrophysics
    • one year ago
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    If your f(x) = 1/(x-5) or is it (1/x)-5

  6. anonymous
    • one year ago
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    it's 1/(x-5)

  7. Astrophysics
    • one year ago
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    Ok, always put brackets! :) So go ahead and find f(g(x)) as I told you how to

  8. anonymous
    • one year ago
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    I got 1/(x^2-3)

  9. Astrophysics
    • one year ago
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    \[f(g(x)) = \frac{ 1 }{ (x^2+2)-5 }\]

  10. anonymous
    • one year ago
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    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
    • one year ago
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    So yes, you're right :)

  12. anonymous
    • one year ago
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    thanks!

  13. Astrophysics
    • one year ago
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    (g o f)(x) is the same thing as g(f(x))

  14. anonymous
    • one year ago
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    oh, so do i just plug in 6 to 1/(x^2-3) ?

  15. Astrophysics
    • one year ago
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    So plug in function f(x) in g(x) then plug in 6 for (g o f)(6)

  16. Astrophysics
    • one year ago
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    No, that's f(g(x))

  17. anonymous
    • one year ago
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    oh so is it 1/(x-5) + 2

  18. Astrophysics
    • one year ago
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    \[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\]

  19. anonymous
    • one year ago
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    Do i need to simplify that? or no

  20. Astrophysics
    • one year ago
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    Just find g(f(6))

  21. anonymous
    • one year ago
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    wait, is Find F(6) just plugging in 6 to f(x)

  22. anonymous
    • one year ago
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    and g(f(6)) is the equation you gave? for part b

  23. Astrophysics
    • one year ago
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    \[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\] \[g(f(6)) = \left( \frac{ 1 }{ 6-5 } \right)^2+2\]

  24. anonymous
    • one year ago
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    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
    • one year ago
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    and there's another question that says find f(6) so would that just be 1

  26. Astrophysics
    • one year ago
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    Can you post the question, it's a bit confusing with all the notation

  27. Astrophysics
    • one year ago
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    Especially when you're not using LaTeX

  28. anonymous
    • one year ago
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    1) Find f(6). 2) Substitute the value you found in Part 1 into g(x) to find g(f(6))

  29. Astrophysics
    • one year ago
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    I mean take an image of the question

  30. Astrophysics
    • one year ago
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    and post it here

  31. anonymous
    • one year ago
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    oh sorry! hold on

  32. Astrophysics
    • one year ago
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    Yeah, I'm not sure which question is connected to what, so it's a bit confusing :P

  33. anonymous
    • one year ago
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  34. anonymous
    • one year ago
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    it was separated into two pages, sorry!

  35. Astrophysics
    • one year ago
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    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
    • one year ago
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    Oh, sorry ignore the graph, it's a different question. sorry!!

  37. Astrophysics
    • one year ago
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    Huh? Then this really makes no sense, are the pages both completely different questions?

  38. anonymous
    • one year ago
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    Nope, they're supposed to go together

  39. Astrophysics
    • one year ago
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    Oh I see, the graph is on a different piece of paper!

  40. anonymous
    • one year ago
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    yeah!! sorry haha :/

  41. Astrophysics
    • one year ago
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    Ok, so lets do it all over again

  42. Astrophysics
    • one year ago
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    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
    • one year ago
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    You can do the simplifications, now lets move on to part 2

  44. Astrophysics
    • one year ago
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    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
    • one year ago
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    1!

  46. Astrophysics
    • one year ago
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    Good

  47. anonymous
    • one year ago
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    and so B would be 3 right?

  48. Astrophysics
    • one year ago
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    Lets see

  49. Astrophysics
    • one year ago
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    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
    • one year ago
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    yup! so I would just find g(f(x)) right?

  51. Astrophysics
    • one year ago
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    What we found in part 1 was \[g(x) = x^2+2\]

  52. Astrophysics
    • one year ago
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    Is the one they are referring to I believe

  53. Astrophysics
    • one year ago
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    So all you need to do here is, find g(f(x)) first then g(f(6))

  54. Astrophysics
    • one year ago
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    \[g(f(x)) = \left( \frac{ 1 }{ x-5 } \right)^2+2\]

  55. anonymous
    • one year ago
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    I got 3

  56. Astrophysics
    • one year ago
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    \[g(f(6)) = \left( \frac{ 1 }{ 6-5 } \right)^2+2\]

  57. anonymous
    • one year ago
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    so yes, 3?

  58. Astrophysics
    • one year ago
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    Yeah

  59. anonymous
    • one year ago
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    Thanks so much for your help!! :))

  60. Astrophysics
    • one year ago
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    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
    • one year ago
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    I get it now haha :) thanks!!

  62. Astrophysics
    • one year ago
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    We could've very well put \[g(f(6)) = f(6)^2 + 2 = 1^2+2\]

  63. Astrophysics
    • one year ago
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    Np

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