Question

Given that f(x) = x2 + 3x + 6 and g(x) = the quantity of x plus two, over three, solve for f(g(x)) when x = 1.

Answer 1

Let's first put g(x) into its algebraic representation.

"The quantity of.." part immediately tells you that you're going to have parenthesis, and that (x+2) is one entity. Then, you need to divide it by 3.

So g(x) = (x+2)/3.

If the question didn't include "the quantity of..", then g(x) would be ambiguous. We could interpret it to be x + 2/3, which is not correct.

Anyway, f(g(x)) says to take every 'x' in f(x), and replace them with the entire function g(x).

So,
\[ f(x) = \left( \frac{x+2}{3} \right)^2 + 3\left(\frac{x+2}{3}\right) + 6. \]
You can simplify it you want.

Answer 2

So i plug in 1?

Answer 3

If i plug in 1 then for g(x) i got 1 and for f(x) i got 10 :o

Answer 4

Oh right it wants it 1. So you don't even need to simplify! That would just waste time.

So yeah f(g(1)) = (3/3)^2 + 3(1+2)/3 + 6 = 1 + 3 + 6 = 10.

That's correct.

Answer 5

but the choices are
A.) -1
B.) 0
C.) 3
D.) 4
So what would i do next?