Q8 / 87 · NTA Abhyas (JEE Main) 2020 · Mathematics · Functions

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

Solution

We have,
$e^{x} + e^{f (x)} = e \Rightarrow e^{f (x)} = e - e^{x}$
$\Rightarrow f (x) = \log (e - e^{x})$
For $f (x)$ to be defined,

$e - e^{x} > 0$
$\Rightarrow e^{1} > e^{x} \Rightarrow x < 1$
$∴$ Domain of $f = (- \infty, 1)$

Hence, the correct answer is option: 'B'.