The domain of the function f(x) = ln(x - [x]) | vedclass

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(A) The function is defined when the argument of the natural logarithm is strictly positive.Thus,we require $x - [x] > 0$.By definition,the fractional

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$R - Z$

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(A) The function is defined when the argument of the natural logarithm is strictly positive.Thus,we require $x - [x] > 0$.By definition,the fractional part of $x$ is denoted as $\{x\} = x - [x]$.The condition $x - [x] > 0$ implies $\{x\} > 0$.The fractional part $\{x\}$ is always non-negative,i.e.,$\{x\} \ge 0$.It is equal to $0$ if and only if $x$ is an integer $(x \in Z)$.Therefore,$\{x\} > 0$ holds for all real numbers except integers.Hence,the domain is $R - Z$.

The domain of the function $f(x) = \ln(x - [x])$ is

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