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Let f(x) = e x – x and g(x) = x 2 – x, ∀ x ∈ R. Then the set of all x ∈ R, where the function h(x) = (fog) (x) is increasing, is :

1. [0, ∞ )
2. ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 1 – , 1 – ∪ ⎟ ⎠ ⎞ ⎢ ⎣ ⎡ ∞ , 2 1
3. ) , 1 [ 0 , 2 1 – ∞ ∪ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡
4. ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 1 , 0 ∪ [1, ∞ )

Correct answer: ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 1 , 0 ∪ [1, ∞ )

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