Describe the relationship between input and output values for composite functions.

Functions are often described in terms of "input" and "output".

Answer: If the composite is fog(x), the output of "g" is the input of "f".

The composition of functions can be analyzed as a box inside a box.

Explanation:

A function can be conceptualized as a black box. The input value x is put in the box and the box performs a specific set of operations on it. Once the operation is complete the output is retrieved. Once the output is retrieved, the box is ready to work on the next input.

Using this idea, function composition can be seen as a box inside of a box. The input x value goes into the inner box, and then the output of the inner box is used as the input of the outer box.

If the composite is fog(x), the output of "g" is the input of "f".

Example:

If f (x) = x + 2, and g (x) = 2x + 4, what is f(g(x))?

f(g(x)) = f(2x + 4) = (2x + 4) + 2 = 2x + 6.

Hence, when we input one function into another, we call this the composition of the two functions.