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Composing Functions

The simple functions –etc – present a very narrow range of possibilities. We can find may more function by composing functions with other functions, obtaining some other function in x, or operating on the result of one function with another function.

For example, ifandthen

It must first be noted that writing a function asoris purely to define the form of the function. The argument of a function is arbitrary. Any expression may be substituted for- a function is defined completely by it's form, so that if we have a functionand we need too find a functionthen we represent all the's in the expression forby's. Ifis also a function of, then we may substitutefor

Example:

Example:

If may be necessary to solve equations involving the composition of two functions, for example

Example:Solve

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