Solve this weird f(g(x)) and g(f(x))

  1. 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?
     
  2. jcsd
  3. nvm i got it now.. the answer is yest
     
  4. 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) = [tex] - \mid x \mid[/tex] and G(x) = [tex] \sqrt{x}[/tex] in that case you would always have the square root of a negative number, but i dont think that is the case in your question.
     
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