Mathematics functions question

>>336760
domain = set of inputs
codomain = set of possible outputs

fg means
>apply g first, then f
In other words: for each number, input it into the function g, and take the output and put it into the function f, and take its output.
gf means
>apply f first, then g

If what you posted is the entire question, it's poorly posed and you should switch to a different school. Otherwise, you're just wasting people's time by not posting all information.

>>336900
No this is the whole question. I'm still slightly confused about what they want me to do with fg and gf because they don't have a function associated to them in the question. Thanks anyway.

it would make sense if it gave info about f and g
so I assume both have domain [-4, 4]
>fg
R(g) must be in D(f)=[-4, 4]
so D(fg) is all x st g(x) in [-4, 4]
R(fg) is a subset of R(f)
fg(x) in R(fg) if x and g(x) in [-4,4]

>>336900
I agree with this anon, the question is poorly posed. You cannot work out the domain of f○g or g○f without given functions.
You can really only say that the domain of (f○g)(x) is all x such that g(x) is within [-4, 4] and that the domain of (g○f)(x) is all x such that f(x) is within [-4, 4]
>>336974
This is probably the closest to an answer.

The answer is whale to the second power