The domain of the function f(x)=sqrt (1-lnx) is D xleqslant e 0leqslant xleqslant e xlt e 0lt xlt e 0lt xleqslant e

## Step 1: Argument of Square Root must be Non-Negative<br />### The argument of the square root must be non-negative, so $1 - \ln x \ge 0$.<br /><br />## Step 2: Simplify the Inequality<br />### Rearranging the inequality gives $\ln x \le 1$.<br /><br />## Step 3: Exponentiate Both Sides<br />### Exponentiating both sides with base $e$ yields $x \le e^1$, or $x \le e$.<br /><br />## Step 4: Consider the Domain of the Logarithm<br />### The domain of $\ln x$ is $x > 0$.<br /><br />## Step 5: Combine the Conditions<br />### Combining $x \le e$ and $x > 0$, we get $0 < x \le e$.