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anonymous

  • one year ago

For the functions f(x) = 2x − 6 and g(x) = 5x + 1, which composition produces the greatest output? Both compositions produce the same output. Neither composition produces an output. f(g(x)) produces the greatest output. g(f(x)) produces the greatest output. @mertsj @jim_thompson5910

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  1. jim_thompson5910
    • one year ago
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    are you able to determine f(g(x)) ?

  2. anonymous
    • one year ago
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    I have trouble with it.

  3. UsukiDoll
    • one year ago
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    maybe we can write it differently like instead of f(g(x)) we can write f o g

  4. UsukiDoll
    • one year ago
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    and for g(f(x)) -> g o f

  5. UsukiDoll
    • one year ago
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    I had to read these questions from right to left when I first did them

  6. jim_thompson5910
    • one year ago
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    to find f(g(x)), you first replace every x with g(x) \[\Large f(x) = 2x - 6\] \[\Large f({\color{red}{g(x)}}) = 2({\color{red}{g(x)}}) - 6\] then on the right side, you replace g(x) with what its definition is. In this case, g(x) = 5x+1 \[\Large f({\color{red}{g(x)}}) = 2({\color{red}{5x+1}}) - 6\] making sense?

  7. anonymous
    • one year ago
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    Kinda, yes

  8. jim_thompson5910
    • one year ago
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    what does 2(5x+1) - 6 simplify to?

  9. UsukiDoll
    • one year ago
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    or how I like to put it ... insert your entire g(x) inside the x of the f(x) \[f(x) = 2x-6\] \[g(x) = 5x+1\] \[2(5x+1)-6\] then use distribution

  10. anonymous
    • one year ago
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    Distribute the 2 in the parenthesis?

  11. jim_thompson5910
    • one year ago
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    yes, then what?

  12. UsukiDoll
    • one year ago
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    distribute the 2 for (5x+1) and then combine like terms

  13. anonymous
    • one year ago
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    Is it possible to multiply 5x by 2?

  14. jim_thompson5910
    • one year ago
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    yes you will multiply the outer 2 by each term inside

  15. UsukiDoll
    • one year ago
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    distribution is multiplication so multiply 2 times 5x and 2 x 1

  16. jim_thompson5910
    • one year ago
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    |dw:1434845209689:dw|

  17. anonymous
    • one year ago
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    (10x + 2)-6

  18. jim_thompson5910
    • one year ago
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    you can toss those parenthesis since they aren't needed

  19. UsukiDoll
    • one year ago
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    correct 10x+2-6 so now we need 2-6

  20. anonymous
    • one year ago
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    -4

  21. UsukiDoll
    • one year ago
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    \[2(5x+1)-6 \rightarrow 10x+2-6 \rightarrow 10x-4\]

  22. UsukiDoll
    • one year ago
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    yes so that's our f(g(x)) or f o g 10x - 4

  23. anonymous
    • one year ago
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    How do I translate that to the answer choices.

  24. UsukiDoll
    • one year ago
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    now we need g(f(x)) or g o f it means place your entire f(x) equation inside the x for g(x) \[f(x) = 2x-6 \] \[g(x) =5x+1\]

  25. jim_thompson5910
    • one year ago
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    are you able to use these steps to figure out g(f(x)) ?

  26. anonymous
    • one year ago
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    can't wait to see the answer to ", which composition produces the greatest output?"

  27. UsukiDoll
    • one year ago
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    maybe after we have the new equation we let x = any number and whoever has the highest number has the highest output idk just guessing

  28. anonymous
    • one year ago
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    this is like the seventh time i have seen this question written by a mathematical illiterate what does "produces the greatest output" mean? it means nothing

  29. UsukiDoll
    • one year ago
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    blame the publishers.

  30. anonymous
    • one year ago
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    I'm really confused.

  31. anonymous
    • one year ago
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    you ought to be !

  32. anonymous
    • one year ago
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    How do I set up g(f(x))?

  33. UsukiDoll
    • one year ago
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    anyway... we need g(f(x)) or g o f which means we place our entire f(x) function into the x's of the g(x) function

  34. UsukiDoll
    • one year ago
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    recall that our functions are f(x) = 2x-6 and g(x) = 5x+1

  35. anonymous
    • one year ago
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    5(2x-6)+1 ?

  36. jim_thompson5910
    • one year ago
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    Start with g(x) and replace EVERY x with f(x) \[\Large g(x) = 5x + 1\] \[\Large g({\color{red}{f(x)}}) = 5({\color{red}{f(x)}}) + 1\]

  37. jim_thompson5910
    • one year ago
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    then on the right side, replace f(x) with 2x-6 so yeah you have it, 5(2x-6) + 1

  38. UsukiDoll
    • one year ago
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    O_O unheard that's right... now we need to distribute and simplify

  39. jim_thompson5910
    • one year ago
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    simplify 5(2x-6) + 1

  40. UsukiDoll
    • one year ago
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    what is 5 times 2x and what is 5 x -6 ?

  41. anonymous
    • one year ago
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    10x+30+1

  42. UsukiDoll
    • one year ago
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    you have a sign error

  43. UsukiDoll
    • one year ago
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    5 multiplied by -6 = ?

  44. anonymous
    • one year ago
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    Oops, yeah, I dont have my glasses on. One sec.

  45. UsukiDoll
    • one year ago
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    xD it's ok.. I had trouble reading my math book last semester.. careless mistakes on my midterms.. xD

  46. anonymous
    • one year ago
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    -30

  47. UsukiDoll
    • one year ago
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    yes \[10x-30+1\]

  48. UsukiDoll
    • one year ago
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    so now what is -30+1 ?

  49. anonymous
    • one year ago
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    -29

  50. UsukiDoll
    • one year ago
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    mhm \[10x-29\] is our g(f(x)) and \[10x-4 \] is our f(g(x))

  51. anonymous
    • one year ago
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    So how does that translate to my answer choices.

  52. anonymous
    • one year ago
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    Which is more?

  53. jim_thompson5910
    • one year ago
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    Let's say x = 0. What is f(g(x)) equal to? What is g(f(x)) equal to?

  54. anonymous
    • one year ago
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    10x-4 10x+-29

  55. jim_thompson5910
    • one year ago
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    in each case, replace x with 0 and compute

  56. UsukiDoll
    • one year ago
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    subsitute x = 0 into both equations

  57. anonymous
    • one year ago
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    0-4 0+-29

  58. UsukiDoll
    • one year ago
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    ok so what's 0-4 and 0-29?

  59. anonymous
    • one year ago
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    4 29

  60. UsukiDoll
    • one year ago
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    uhhhhh... no... that's positive numbers... we are dealing with negative numbers

  61. UsukiDoll
    • one year ago
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    think of it as ... you are charged $4 but don't have any money ... you have a negative balance

  62. anonymous
    • one year ago
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    -4 -29

  63. UsukiDoll
    • one year ago
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    yes :)

  64. UsukiDoll
    • one year ago
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    now... bigger negative numbers are much smaller in value than single digit negative numbers

  65. anonymous
    • one year ago
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    so, f(g(x))!!

  66. UsukiDoll
    • one year ago
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    yeah... -4 is bigger than -29

  67. anonymous
    • one year ago
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    Thank you.

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