Question

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Answer 1

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.

Answer 2

your g(x) looks a little off. should there be parentheses around the x+4?

Answer 3

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)

Answer 4

if \[\Large g(x) = \frac{x+4}{3}\] then what is g(2)?

Answer 5

Replace every x with 2. Then evaluate
\[\Large g(\color{red}{x}) = \frac{\color{red}{x}+4}{3}\]
\[\Large g(\color{red}{2}) = \frac{\color{red}{2}+4}{3}\]
\[\Large g(2) = ??\]

Answer 6

2 is just one of the steps to get to the answer

Answer 7

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))

Answer 8

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)
\[\Large f(x) = x^2 + 2x + 3\]
\[\Large f(2) = 2^2 + 2*2 + 3\]
\[\Large f(2) = ??\]

Answer 9

yes

Answer 10

Since f(2) = 11, this means f(g(2)) = 11

Answer 11

I'm glad it's clicking now