The domain of $f (x)$ is $[0, 1]$ , then the domain of $y = f (e^{x}) + f (| [x] |)$ is
(where [.] denotes greatest integer function)

(- e, - 1)

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[- 1, 0]

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(- \infty, 2)

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[- 1, 0] \cap [0, 1]

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Solution

The correct option is B $[- 1, 0]$
For domain of $y$
$0 \leq e^{x} \leq 1$ and $0 \leq | [x] | \leq 1$
$- \infty < x \leq 0 \cap - 1 \leq [x] \leq 1$
$- \infty < x \leq 0 \cap - 1 \leq x < 2$
So, the intersection is $- 1 \leq x \leq 0$

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