1. ## Functions

I don't know where I'm going with this. I think my reasoning is out of whack, can someone please explain this to me?

Alright, so when f(x)=3, the x is a 1. And when x is a one over at the g(x) side where x is, it's a -1. So -1 x 3 = -3...B.

2. Originally Posted by A Beautiful Mind
I don't know where I'm going with this. I think my reasoning is out of whack, can someone please explain this to me?

Alright, so when f(x)=3, the x is a 1. And when x is a one over at the g(x) side where x is, it's a -1. So -1 x 3 = -3...B.
We aren't looking for when $\displaystyle f(x)=3$, we are looking for the value of $\displaystyle f(x)$ AT $\displaystyle x=3$ Look at the table, and at $\displaystyle x=3$ we see that $\displaystyle f(x)=2$ which means that $\displaystyle f(3)=2$. Now because we have $\displaystyle g(f(3))$, we need to find $\displaystyle g(x)$ AT $\displaystyle f(3)=2$. So the question is essentially asking for $\displaystyle g(2)=?$

Looking at the table we see that $\displaystyle g(f(3))=g(2)=-3$ which is answer choice B.

Is another way to look at it.

3. Nah, I got it. Thanks.