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)=32+1=10, we have




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)g(x), and, assuming g(x)0, f(x)/g(x). We use the notation shown below. ...

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