Can You Compute Compositions f(g(x)) and g(f(x)) with Given Functions?

[Euphoriet]

Can you solve such a thing as:
f(g(x)) and g(f(x))

Let f(x) = sqr (4-x)
D=x < or = to 4 right?
and
also Let g(x) = sqr(x-3)

D = x > or = to 3

Can you solve such a thing.. if so how.. if not why not?

 

[Euphoriet]

nvm i got it now.. the answer is yest

 

[T@P]

the composition of functions F(G(x)) can be done like this: find G(x) in terms of x, then pretend your result is like 'x' and plug it into F(x) . ultimately the domain and range of your function will change since the new function F(G(x)) will be a totally new function, there may be cases when it is impossible to find F(G(x)).

for example, of F(x) = $$- \mid x \mid$$ and G(x) = $$\sqrt{x}$$ in that case you would always have the square root of a negative number, but i don't think that is the case in your question.