If e^{x}+e^{f(x)}=e, then the domain of f(x) is

Correct Answer is : (−∞,1)(-∞, 1)(−∞,1)

Correct Answer is : (−∞,1)(-∞, 1)(−∞,1)

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MHTCET 16 Apr 2026 Shift 2 Paper

Question : 119 of 150

Marks: +1, -0

e^{x}+e^{f(x)}=e

f(x)

Solution:

Concept:

For

f(x)

to be real,

e^{f(x)}

must be positive.

Explanation:

Given

e^{x}+e^{f(x)}=e

, isolate

e^{f(x)}

e^{f(x)}=e-e^{x}

Since

e^{f(x)} > 0

for every real

f(x)

, the right side must also be positive:

e-e^{x} > 0

e > e^{x}

The exponential function is strictly increasing, so:

1 > x

x < 1

x = 1

, we get

e^{f(x)} = e - e = 0

, which is impossible because an exponential function is never zero.

Hence,

x = 1

is excluded from the domain.

Answer:

The domain of

f(x)

(-\infty, 1)

, so the correct option is B.

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