Compositions of Functions
Take for example the functions , and , does the composition exist? What about ?
The two functions are graphed below, evaluate .
Can you write a general expression for ? What about ?
Which composition exists without any changes? Which composition has to have the domain/target modified?
What changes are necessary?
With that in mind, do you think the following statement is true or false? "If we compose two functions f(x) and g(x), we always have , for all values of x."