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

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(A) The function $f(x) = \log_e(x - [x])$ is defined when the argument of the logarithm is strictly positive.So,we require $x - [x] > 0$.We know that

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$R - Z$

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(A) The function $f(x) = \log_e(x - [x])$ is defined when the argument of the logarithm is strictly positive.So,we require $x - [x] > 0$.We know that the fractional part function is defined as $\{x\} = x - [x]$.The range of the fractional part function is $[0, 1)$.For $\log_e(\{x\})$ to be defined,we need $\{x\} > 0$.Since $\{x\} = 0$ when $x$ is an integer $(x \in Z)$,the function is undefined for all integers.For all non-integer values $(x \in R - Z)$,$\{x\} > 0$.Therefore,the domain of the function is $R - Z$.

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

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