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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$R - Z$

Vedclass · Answer

(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

Similar Questions

If the range of the real valued function $f(x) = \frac{x^2+x+k}{x^2-x+k}$ is $\left[\frac{1}{3}, 3\right]$,then $k=$

The domain and range of $y(x) = \cos x - 3$ are respectively

Domain of the function $\log |x^2 - 9|$ is

If $f:R \to S$ defined by $f(x) = \sin x - \sqrt{3} \cos x + 1$ is onto,then the interval of $S$ is

The range of the real valued function $f(x) = \frac{15}{3 \sin x + 4 \cos x + 10}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module