open_studier
  • open_studier
.......
Mathematics
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open_studier
  • open_studier
.......
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
This is a function machine. You have to in put the x=2 into g function first before you can input into the f function. The answer from your g becomes the x for you f function.
anonymous
  • anonymous
your g(x) looks a little off. should there be parentheses around the x+4?
jim_thompson5910
  • jim_thompson5910
To write out \(\LARGE \frac{x+4}{3}\) on the keyboard, you would type `(x+4)/3`. The parenthesis are important because you are dividing ALL of `x+4` by `3` (not just the 4 over 3)

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jim_thompson5910
  • jim_thompson5910
if \[\Large g(x) = \frac{x+4}{3}\] then what is g(2)?
jim_thompson5910
  • jim_thompson5910
Replace every x with 2. Then evaluate \[\Large g(\color{red}{x}) = \frac{\color{red}{x}+4}{3}\] \[\Large g(\color{red}{2}) = \frac{\color{red}{2}+4}{3}\] \[\Large g(2) = ??\]
jim_thompson5910
  • jim_thompson5910
2 is just one of the steps to get to the answer
jim_thompson5910
  • jim_thompson5910
we start with f(g(x)) we want to evaluate this at x = 2. So replace x with 2 we want to evaluate f(g(2))
jim_thompson5910
  • jim_thompson5910
f(g(2)) is the same as f(2) since g(2) = 2. We can replace the `g(2)` with `2` because they are equal. Now plug x = 2 into f(x) \[\Large f(x) = x^2 + 2x + 3\] \[\Large f(2) = 2^2 + 2*2 + 3\] \[\Large f(2) = ??\]
jim_thompson5910
  • jim_thompson5910
yes
jim_thompson5910
  • jim_thompson5910
Since f(2) = 11, this means f(g(2)) = 11
jim_thompson5910
  • jim_thompson5910
I'm glad it's clicking now

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