Composite Functions

I want to know how to do this problem too.....

This is not likely to be a very good 'proof' but here goes.

since f(x) and g(x) are odd funtion,

$f(-x)=-f(x)$            and      $g(-x)=-g(x)$

Let  $x_1$  be a point such that    

$a=g(x_1)   \qquad     -a=g(-x_1)$

$f(g(x_1))=f(a) \qquad f(g(-x_1))=f(-g(x_1))=f(-a)=-f(a)\\ so\\ f(-g(x_1))=-f(g(x_1)) \\ \text{by definition this means that }f(g(x)) \text{ is an odd function.}$