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, if
and
then
It must first be noted that writing a function as
or
is 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 function
then 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
