Composites and Numbers

What happens when numbers are substituted into a composite function? As you saw in the function machine demo, the number is substituted in one function, then the result of that calculation is fed into the second function.

For example, if f(x) = 3x+1 and g(x) = 5x², then f(g(-2)) would be evaluated as follows:

1. Substitute -2 into g(x); that is find g(-2).

g(x) = 5x²
g(-2) = 5•(-2)²
         = 5 • 4
         = 20
     

2. Now take the result from g(-2) or 20 and substitute that value into f(x).

f(x) = 3x + 1
f(g(-2)) = 3•(g(-2)) + 1
              = 3•(20) + 1
              = 61
    

3. Another way to do evaluate f(g(-2)) is to find f(g(x)) then substitute -2 into that composite function. For example:

f(x) = 3x + 1        g(x) = 5x²

f(g(x)) = 15x² + 1
f(g(-2)) = 15•(-2)² + 1
              = 15•4 + 1
              = 61