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 :

Question

Let f(x) = e^x – 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 :

[0, $\infty $)

$\left[ { - 1, - {1 \over 2}} \right] \cup \left[ {{1 \over 2},\infty } \right)$

$\left[ { - {1 \over 2},0} \right] \cup \left[ {1,\infty } \right)$

$\left[ {0,{1 \over 2}} \right] \cup \left[ {1,\infty } \right)$

Solution

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