Question 214738
Which composition(s) do you have to find? Do you have to find (f o g)(x) or (g o f)(x)? Or do you have to find (f o f)(x) or (g o g)(x)? Or is it something entirely different?



Finding (f o g)(x)



{{{f(x)=(3-x)^(1/2)^""}}} Start with the given function.



{{{f(g(x))=(3-(x^2-16)^(1/2))^(1/2)^""}}} Plug in {{{g(x)=(x^2-16)^(1/2)}}}



Since not much simplification is possible at this point, our answer is 



{{{f(g(x))=(3-(x^2-16)^(1/2))^(1/2)^""}}}



Note: you may want to covert to radical notation to get



{{{f(g(x))=sqrt(3-sqrt(x^2-16))}}}



This of course would depend on the book's/worksheet's/teacher's instructions.