Composites and Numbers: Ordering
If you were asked to find g(f(-2)), you would substitute -2 into f(x) first, then take that result and input into g(x).
For example, if f(x) = 3x+1 and g(x) = 5x2, then g(f(-2)) would be evaluated as follows:
1. Substitute -2 into f(x); that is find g(-2).
f(x) = 3x + 1
f(-2) = 3•(-2) + 1
= -5
2. Now take the result from f(-2) or -5 and substitute that value into g(x).
g(x) = 5x2
g(f(-2)) = 5•(g(-2))2
= 5•(-5)2
= 5 • 25
= 125
3. Another way to do evaluate g(f(-2) is to find g(f(-2)) then substitute -2 into that composite function. For example:
f(x) = 3x + 1 g(x) = 5x2
g(f(x)) = 5•(3x + 1)2
g(f(-2)) = 5•((3•(-2) +1)2
= 5•(-6 + 1)2
= 5•(-5)2
= 5•25
= 125
