WBJEE · Maths · Functions
The domain of definition of the function \(f(x)=\sqrt{1+\log _{\mathrm{e}}(1-x)}\) is
- A \(-\infty < x \leq 0\)
- B \(-\infty < x \leq \frac{e-1}{e}\)
- C \(-\infty < x \leq 1\)
- D \(x \geq 1-e\)
Answer & Solution
Correct Answer
(B) \(-\infty < x \leq \frac{e-1}{e}\)
Step-by-step Solution
Detailed explanation
Hints : \(1-x>0 \Rightarrow X < 1\) \[ \begin{aligned} & 1+\log _e(1-x) \geq 0 \\ & \log _e(1-x) \geq-1 \Rightarrow 1-x \geq e^{-1} \\ & x \leq 1-\frac{1}{e} \\ & x \leq \frac{e-1}{e} \end{aligned} \]
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