SOLUTION: Consider the functions {{{f(x) = 3x^2 + 1}}} and {{{g(x) = x + 3}}}. What is the value of f[g(-1)]?

Question 465784: Consider the functions and . What is the value of f[g(-1)]?

Answer by kingme18(98) (Show Source): You can put this solution on YOUR website!
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. , so . 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. , so . 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.
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