If \( e^{x}+e^{f(x)}=e \), then for \( f(x) \) : (a) Domain is \( (-\infty, 1) \) (b) Range is \...

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If \( e^{x}+e^{f(x)}=e \), then for \( f(x) \) :
(a) Domain is \( (-\infty, 1) \) (b) Range is \( (-\infty, 1] \)
(c) Domain is \( (-\infty, 0] \) (d) Range is \( (-\infty, 0] \)
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