Thread: Composite functions

If

The question requires the function

I've worked out , which is given by


Obviously is undefined when .

My question is whether is defined when

Even though the expression is defined when , is not defined at since is not defined at , am I correct?

Originally Posted by acc100jt

If

The question requires the function

I've worked out , which is given by


Obviously is undefined when .

My question is whether is defined when

Even though the expression is defined when , is not defined at since is not defined at , am I correct?

I do not understand the notation that you have employed. What do you mean by ?

compose h with itself, i.e.

Originally Posted by acc100jt

compose h with itself, i.e.

Oh. Well, then no, a restriction at x=1 must be made because of the way we have defined .

We can't get passed through x=1. This means we'd never get to . This is subtle, but it is the case when dealing with functions.

Originally Posted by VonNemo19

Oh. Well, then no, a restriction at x=1 must be made because of the way we have defined .

You mean, "Well, then yes" since he was asking if it was correct that the function was NOT defined at x= 1!

We can't get passed through x=1. This means we'd never get to . This is subtle, but it is the case when dealing with functions.