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anonymous

  • one year ago

WILL BECOME FAN AND AWARD MEDAL!!! Make up any two functions f(x) and g(x), defined in terms of the variable x. For example, you might define f(x) = x – 15 and g(x) = 3x2. (Use different examples.) Then provide the compositions of the two functions f(g(x)) and g(f(x)). Which composite function has the greatest value for x = 10? Remember no right answer exists. Your answer completely depends on the functions you select.

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  1. anonymous
    • one year ago
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    did you pick two functions?

  2. anonymous
    • one year ago
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    go ahead and make two up they can be anything, but you don't want to make them too hard, so stick with something simple

  3. anonymous
    • one year ago
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    once you have them we can do this easy

  4. anonymous
    • one year ago
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    f(x)= x+7 and g(x)= 1/x+7 were the functions I thought to use for this.

  5. anonymous
    • one year ago
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    \[f(x)=x+7,g(x)=\frac{1}{x+7}\] like that?

  6. anonymous
    • one year ago
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    or was \(g(x)=\frac{1}{x}+7\) either way we can do it

  7. anonymous
    • one year ago
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    you pick

  8. anonymous
    • one year ago
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    the second one was how I meant to put the second function. sorry ^.^"

  9. anonymous
    • one year ago
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    ok brave to use a denominator but no problem lets compute \[f(g(x))\] first

  10. anonymous
    • one year ago
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    always work from the inside out \[f(g(x))=f(\frac{1}{x}+7)\] is a fist step

  11. anonymous
    • one year ago
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    then since \(f9\heartsuit)=\heartsuit +7\) you have ' \[f(\frac{1}{x}+7)=\frac{1}{x}+7+7\] or more simply \[\frac{1}{x}+14\]

  12. anonymous
    • one year ago
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    \[f(x)=x+7\] and \[g(x)= \frac{ 1}{ x } +7\] this is how they should look

  13. anonymous
    • one year ago
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    yeah got it

  14. anonymous
    • one year ago
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    that makes \[f(g(x))=f(\frac{1}{x}+7)=\frac{1}{x}+7+7=\frac{1}{x}+14\]

  15. anonymous
    • one year ago
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    Sorry. My computer is messing up so I'm having a hard time seeing your responses. I'm not sure why open study isn't working properly for me, but it isn't...

  16. anonymous
    • one year ago
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    yeah for me too

  17. anonymous
    • one year ago
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    did you see the last one?

  18. anonymous
    • one year ago
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    Yes! And thank you for your help! I really do appreciate it :3

  19. anonymous
    • one year ago
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    for the next one it is a bit tricker

  20. anonymous
    • one year ago
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    \[g(f(x))=g(x+7)=\frac{1}{x+7}+7\]

  21. anonymous
    • one year ago
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    you can replace \(x\) by 10 in both of those for \[g(f(10))\] you will get \[\frac{1}{10+7}=7=\frac{1}{17}+7=7\tfrac{1}{17}\]

  22. anonymous
    • one year ago
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    you mean to get the result for Which composite function has the greatest value for x=10?

  23. anonymous
    • one year ago
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    right

  24. anonymous
    • one year ago
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    Sorry >.< late response again. But I believe I understand the material. ^w^

  25. anonymous
    • one year ago
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    ok good stay cool

  26. anonymous
    • one year ago
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    You too! ^w^ Thanks for the help @satellite73 :3

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