anonymous
  • anonymous
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
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
i will medal
zepdrix
  • zepdrix
Hey William :)\[\large\rm \color{orangered}{f(x)=6x+12},\qquad\color{royalblue}{g(x)=x-8}\]
zepdrix
  • zepdrix
Hmm so we need to solve this:\[\large\rm \color{orangered}{f\left[\color{royalblue}{g(6)}\right]}\]

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More answers

zepdrix
  • zepdrix
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?
anonymous
  • anonymous
so you say to turn it into g(x)=6-8?
zepdrix
  • zepdrix
Good, yes.\[\large\rm g(x)=x-8,\qquad g(6)=6-8\]Looks like we end up with -2, ya?
zepdrix
  • zepdrix
So then,
zepdrix
  • zepdrix
That simplifies down the blue inner part for us. \[\large\rm \color{orangered}{f\left[\color{royalblue}{g(6)}\right]}=\color{orangered}{f\left[\color{royalblue}{-2}\right]}\]
zepdrix
  • zepdrix
So now all we need to do is simply plug -2 into our f function.
anonymous
  • anonymous
im having trouble someone talk me through this
anonymous
  • anonymous
hello?
anonymous
  • anonymous
is it f(x)=6(-2) +12
jim_thompson5910
  • jim_thompson5910
yes now evaluate 6(-2) + 12 and you're done
jdoe0001
  • jdoe0001
hmmm what would you get for say \(\bf {\color{brown}{ g(6)}}?\)
anonymous
  • anonymous
0
jdoe0001
  • jdoe0001
0? how.. did you get 0 though?
jdoe0001
  • jdoe0001
anyhow \(\bf g(x)=x-8\qquad g({\color{brown}{ 6}})={\color{brown}{ 6}}-8\)
anonymous
  • anonymous
|dw:1438904530281:dw|
jdoe0001
  • jdoe0001
hmmm ok... wondering where the -2 came from
jim_thompson5910
  • jim_thompson5910
@jdoe0001 the -2 is from g(6) = 6-8 = -2
jdoe0001
  • jdoe0001
hmm maybe I missed something. lemme recheck
jdoe0001
  • jdoe0001
ohh hmm
jdoe0001
  • jdoe0001
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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