f(g(x)) etc.

[geoff_821]

What are the requirements for f(g(x)) to exist?

[taqi]

range of g(x) must be equal to or part of the doman of f(x)

[thatisanote]

which you write like ran g(x) <= (imagine a stretched c with an equals to) dom f(x)
where g(x) is the part inside the composite fn.

[david10d]

what is the domain/range of f(g(x))

[Vincezor]

Domain of f(g(x)) = dom g(x)

Range depends.. I think you have to work that one out using the domain...

[daliu]

For f(g(x))

The range of g(x) must be restricted to the domain of f(x).

However, the overall domain of f(g(x)) is this restricted domain of g(x).

(Also, remember (f+g)(x)=f(x) + g(x) where the domain of (f+g) is dom f n dom g)

and (fg)(x)=f(x)g(x) where the domain of (fg) is dom f n dom g)

[abeybaby]

range of f(g(x)) is the range of f over a domain of ran g.

[daliu]

It's amazing that you asked this question since it just came up on the Methods exam...lucky.