Let f(x) = ex - x and g(x) = x2 - x, ∀x ∈ R. Then the set of all x ∈ R, where the function h(x) = (f o g)(x) is increasing is:

The correct option is B [0, 1/2] ∪ [1, ∞)
h(x) = f(g(x)) ⇒ h'(x) = f'(g(x)).g'(x) and f'(x) = ex - 1; ⇒ h'(x) = (eg(x) - 1)g'(x) ⇒ h'(x) = (ex²-x - 1)(2x - 1) ≥ 0
If 2x - 1 > 0 ⇒ x > 1/2, then ex²-x -1 ≥ 0 ⇒ x² - x ≥ 0 ⇒ x(x - 1) ≥ 0 ⇒ x ≤ 0 or x ≥ 1.
Thus x ≥ 1.
If 2x - 1 < 0 ⇒ x < 1/2, then ex²-x - 1 ≤ 0 ⇒ x² - x ≤ 0 ⇒ x(x - 1) ≤ 0 ⇒ 0 ≤ x ≤ 1.
Thus 0 ≤ x < 1/2.
Combining both cases, we get [0, 1/2) ∪ [1, ∞). However, since the question is asking for the set where h(x) is *increasing*, and we've found the intervals where h'(x) >= 0, we need to include the endpoints where h'(x) = 0. This gives us the final answer: [0, 1/2] ∪ [1, ∞).