Question 465784
f[g(-1)] is called a composition of functions, and it's read "f of g of -1".  I like to say to myself, "what letter is closest to -1?"  That's g, so we'll deal with g first.  We're going to find g(-1), which means we're going to plug -1 into the g function--wherever we see x, we're going to write -1.  {{{g(x)=x+3}}}, so {{{g(-1)=-1+3=2}}}.  So, g(-1)=2.


The original question said f[g(-1)].  We just found out that g(-1)=2, so instead of saying f[g(-1)], we could just say f(2).  This means that we're going to plug 2 into the f function.  {{{f(x)=3x^2+1}}}, so {{{f(2)=3*2^2+1=3*4+1=12+1=13}}}.  So, f(2)=13, which is your final answer.


When you see a composition of functions like this, work your way out; each time, plug the answer you get into the next function out.  Here, we started with the g function, then we took our answer and plugged that into the f function.