Hey guys, I am just confused on these types of questions.
Say if you have a composite function: h(x) = f(g(x)) and you are given an implied domain and an implied range, how do you find out if a number is an element of the domain and range of the outer and inner function?
For example, if the composite function had an implied domain of [2, 6] and implied range of [-1, infinite) how would you find out if 5 is an element of dom(f) and dom(g) and say 6 is an element of ran(g)?
What would be the right method to solve this problem?
Ah, no we can't, at least not if we're assuming and .
is not defined for any , so that means does not exist for any which are negative. In this case for to exist, we require restricting the domain of so that the range will be .