Adding Another Function

Composite functions can be evaluated with any combination of functions. Let's add a third function, h(x) = 2x to f(x) = 3x+1 and g(x) = 5x² and calculate some composites.

1. The composite function f(h(x)) would be:

f(h(x)) = 3•(g(x)) + 1
            = 3•(2x) +1
            = 6x + 1

2. The composite function g(h(x)) would be:

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

3. The composite function h(f(x)) would be:

h(f(x)) = 2•(f(x))
             = 2•(3x+1)
             = 6x + 2