If \( e^{x}+e^{f(x)}= \) e then for \( f(x) \) \( \mathrm{P} \) (a)...

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If \( e^{x}+e^{f(x)}= \) e then for \( f(x) \)
\( \mathrm{P} \)
(a) domain \( =(-\infty, 1) \)
(b) range \( =(-\infty, 1) \)
(c) domain \( =(-\infty, 0] \)
(d) range \( =(-\infty, 1] \)
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