Sketch the graphs of and . Use the graphs to evaluate . What about ? (Solution)
Compositions
Another useful and important way of combining functions is to form the composition. Functions are composed when the output of one function is used as the input for a second function.
The composition of and , written , is the new function . In a composition of functions, the output of the first function is the input of the second.
Examples
Let and let . What function is ? What about ? What about ? (Solution)
Let and . Find and determine its domain. (Solution)
Let and . Find and completely simplify . What is the domain of the composition? (Solution)
A large spherical balloon is being inflated so that its radius, in feet, after minutes is given by . Find its volume as function of . (Solution)
An object is cooling in such a way that its temperature in degrees Celsius after minutes is given by . The formula is used to convert from temperatures in Celsius to Fahrenheit. Find the temperature of the object in degrees Fahrenheit at time . (Solution)
For further help...
Do a Google search for "operations on functions" and/or "compositions of functions".