JEE Math Practice Question

Let f(x) = ex – x and g(x) = x2 – x, $$\forall $$ x $$ \in $$ R. Then the set of all x $$ \in $$ R, where the function h(x) = (fog) (x) is increasing, is :

1. A.[0, $$\infty $$)
2. B.$$\left[ { - 1, - {1 \over 2}} \right] \cup \left[ {{1 \over 2},\infty } \right)$$
3. C.$$\left[ { - {1 \over 2},0} \right] \cup \left[ {1,\infty } \right)$$
4. D.$$\left[ {0,{1 \over 2}} \right] \cup \left[ {1,\infty } \right)$$