open_studier one year ago .......

1. 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.

2. anonymous

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

3. 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)

4. jim_thompson5910

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

5. jim_thompson5910

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

6. jim_thompson5910

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

7. 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))

8. 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) $\Large f(x) = x^2 + 2x + 3$ $\Large f(2) = 2^2 + 2*2 + 3$ $\Large f(2) = ??$

9. jim_thompson5910

yes

10. jim_thompson5910

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

11. jim_thompson5910