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anonymous

  • one year ago

Given the following functions f(x) and g(x), solve f[g(6)] and select the correct answer below: f(x) = 6x + 12 g(x) = x − 8 −96 0 24 48

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  1. anonymous
    • one year ago
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    i will medal

  2. zepdrix
    • one year ago
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    Hey William :)\[\large\rm \color{orangered}{f(x)=6x+12},\qquad\color{royalblue}{g(x)=x-8}\]

  3. zepdrix
    • one year ago
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    Hmm so we need to solve this:\[\large\rm \color{orangered}{f\left[\color{royalblue}{g(6)}\right]}\]

  4. zepdrix
    • one year ago
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    We want to work from the inside and move outward. So let's deal with the blue first. What is the value of the function g, when 6 is plugged in for x?

  5. anonymous
    • one year ago
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    so you say to turn it into g(x)=6-8?

  6. zepdrix
    • one year ago
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    Good, yes.\[\large\rm g(x)=x-8,\qquad g(6)=6-8\]Looks like we end up with -2, ya?

  7. zepdrix
    • one year ago
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    So then,

  8. zepdrix
    • one year ago
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    That simplifies down the blue inner part for us. \[\large\rm \color{orangered}{f\left[\color{royalblue}{g(6)}\right]}=\color{orangered}{f\left[\color{royalblue}{-2}\right]}\]

  9. zepdrix
    • one year ago
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    So now all we need to do is simply plug -2 into our f function.

  10. anonymous
    • one year ago
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    im having trouble someone talk me through this

  11. anonymous
    • one year ago
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    hello?

  12. anonymous
    • one year ago
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    is it f(x)=6(-2) +12

  13. jim_thompson5910
    • one year ago
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    yes now evaluate 6(-2) + 12 and you're done

  14. jdoe0001
    • one year ago
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    hmmm what would you get for say \(\bf {\color{brown}{ g(6)}}?\)

  15. anonymous
    • one year ago
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    0

  16. jdoe0001
    • one year ago
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    0? how.. did you get 0 though?

  17. jdoe0001
    • one year ago
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    anyhow \(\bf g(x)=x-8\qquad g({\color{brown}{ 6}})={\color{brown}{ 6}}-8\)

  18. anonymous
    • one year ago
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    |dw:1438904530281:dw|

  19. jdoe0001
    • one year ago
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    hmmm ok... wondering where the -2 came from

  20. jim_thompson5910
    • one year ago
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    @jdoe0001 the -2 is from g(6) = 6-8 = -2

  21. jdoe0001
    • one year ago
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    hmm maybe I missed something. lemme recheck

  22. jdoe0001
    • one year ago
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    ohh hmm

  23. jdoe0001
    • one year ago
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    well, then \(\bf f(x)=6x+12\qquad f({\color{brown}{ g(6)}})=6[{\color{brown}{ g(6)}}]+12 \\ \quad \\ {\color{brown}{ g(6)}}=-2\qquad then\\\ \quad \\ f({\color{brown}{ g(6)}})=6[{\color{brown}{ g(6)}}]+12\implies f({\color{brown}{ -2}})=6[{\color{brown}{ -2}}]+12\to 0\)

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