Function Composition

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In this section, we learn about function composition. Function composition is where we plug in one function as the input for another function. The notation for this will vary, but in most cases, we see f(g(x)), (f ○ g)(x), or f[g(x)]. This notation is telling us to plug the function g(x) in for x in the function f(x). We then want to simplify and present our answer. As an example, suppose f(x) = x + 5, and g(x) = x - 3. If we were asked for f(g(x)), we would plug in the value of g(x) or (x-3) in for x in f(x) = x + 5. This gives us f(g(x)) = (x - 3) + 5, which simplifies to x + 2. Therefore we can say f(g(x)) = x + 2. In some cases, we will be given a value for the input in the inside function. As an example, suppose we now see f(g(7)). In this case, we can first find g(7), this would give us: g(7) = 7 - 3 = 4. Now we can take g(7) or the value of 4 and use it as the input in the function f, so f(4) = 4 + 5 = 9. This gives us our final answer of: f(g(7)) = 9.
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