Posted by Jeromino on Thursday, March 31, 2011 at 2:35am.
f(x)= 3x5 and g(x)= 2x^2 evaluate:
1.(fog)(x)
2.(gog)(2)

math  Jai, Thursday, March 31, 2011 at 2:54am
(fog)(x) means you substitute the whole function of g(x) into the f(x),, we can actually rewrite this (fog)(x) as f(g(x))  i think this one is clearer.
now let's substitute g(x) to f(x):
(fog)(x) = f(g(x)) = 3x5 = 3[g(x)]  5
(fog)(x) = 3(2  x^2)  5
(fog)(x) = 6  3x^2  5
(fog)(x) = 3x^2 + 1
for #2, we do the same,, we substitute g(x) to g(x) then we evaluate the simplified expression at x=2:
(gog)(x) = g(g(x)) = 2  (g(x))^2
(gog)(x) = 2  (2  x^2)^2
(gog)(2) = 2  [2  (2)^2]^2
(gog)(2) = 2  [2  4]^2
(gog)(2) = 2  (2)^2
(gog)(2) = 2  4
(gog)(2) = 2
hope this helps~ :) 
math  Anonymous, Thursday, March 31, 2011 at 2:57am
Thanks a bunch

math  Jeromino, Thursday, March 31, 2011 at 2:58am
Yes thank you very much!