Calculus I using LiveMath

Chapter 1

Function Algebra & Composite Functions

Another use of the Function Op and Wildcard Variables is when you form new functions, by algebraic manipulation, and by combining functions. In other words, having one act on the other (called Composite Functions). As you study calculus, you will be asked to combine functions in various ways. The rules used are listed below.

Below is an example using LiveMath to perform function algebra.

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• Create a new Prop and set your combination function equal to a new variable. In this example below y is used. If asked, define g and f as a User Defined Functions.

• Substitute both functions into the third Prop.

Try setting up three more Props to perform the other rules.

Composite Functions

A composite function is the single function produced by the composition of two or more functions. Think of one function acting on the other. One function is the inside function and the other is the outside function.

Additionally, anytime you see one function nested inside another you can, for the most part, assume this is the result of combining two or more functions. Being able to recognize this nesting is important when you study integration.

Try making a composite function from the two you just used.

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• Enter a new Prop defining the composite function .

• Substitute the two original functions into this new composite function. Notice how two substitutions are required.