Consider a function f {\displaystyle f} such that f ( x ) < 0 {\displaystyle f(x)<0} for x > 0 {\displaystyle x>0} and f ( x ) > 0 {\displaystyle f(x)>0} for x < 0 {\displaystyle x<0} . Let g ( x ) = x 2 {\displaystyle g(x)=x^{2}} .
Determine the sign of the composite function f ( g ( x ) ) {\displaystyle f(g(x))} if x > 0 {\displaystyle x>0} and if x < 0 {\displaystyle x<0} .
