Composite function by definition
I found this expression on Wikipedia:
If , then ,
where and are identity functions.
I wanted to see whether it's true. So I rewrite the expression using the definition of composite function.
for , , , and .
I replaced with in and replaced with , where . So I wrote the expression for the LHS
Let and , where and .
, but now my difficulty being that I don't know how to express the RHS
I can't find any information anywhere on the web proving .
Could someone please show me how to write the expression for the RHS?