# 2.2 The Algebra of Functions

Find the sum, the difference, the product, and the quotient of two functions, and determine the domains of the resulting functions.

Find the difference quotient for a function.

# The Algebra of Functions: Sums, Differences, Products, and Quotients

We now use addition, subtraction, multiplication, and division to combine functions and obtain new functions.

Consider the following two functions `f` and `g`:

Since $f(3)=3+2=5$ and $g(3)={3}^{2}+1=10$, we have

and

In fact, so long as `x` is in the domain of *both* `f` and `g`, we can easily compute $f(x)+g(x)$, $f(x)-g(x)$, $f(x)\cdot g(x)$, and, assuming $g(x)\ne 0$, $f(x)/g(x)$. We use the notation shown below. ...

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