# Given f(2)=3, f(3)=4, f(5)=0, g(2)=5, g(3)=2, g(4)=-1, how do you evaluate f(g(2))?

Oct 29, 2017

$f \left(g \left(2\right)\right) = f \left(5\right) = 0$

#### Explanation:

It's all about taking this one step at a time, and not getting freaked out by the scary-looking composition.

So, given your information, you need to find $f \left(g \left(2\right)\right)$. Let's start by working inside-out, and finding $g \left(2\right)$.

It's given that $g \left(2\right) = 5$. Now, just plug that back in. This will leave you with $f \left(5\right)$.

And of course, it is also given that $f \left(5\right) = 0$, so your final answer is simply $0$.

Make sure you understand compositions of functions well -- they will come back in a big way when you start calculus!

Hope that helped :)