4 8 composition of functions homework

In this way, we can think of adding, subtracting, multiplying, and dividing functions. For two functions f(x) and g(x) with real number outputs, we define new functions f + g, f − g, fg, and f g by the relations Find and simplify the functions (g − f)(x) and (g f)(x), given f(x) = x − 1 and g(x) = x2 − 1.

Decompose a composite function into its component functions. Suppose we want to calculate how much it costs to heat a house on a particular day of the year. The cost to heat a house will depend on the average daily temperature, and in turn, the average daily temperature depends on the particular day of the year.

By combining these two relationships into one function, we have performed function composition, which is the focus of this section. Function composition is only one way to combine existing functions. Another way is to carry out the usual algebraic operations on functions, such as addition, subtraction, multiplication and division.

The process of combining functions so that the output of one function becomes the input of another is known as a composition of functions. The resulting function is known as a composite function.