The Domain of function $f(x)=\log _e(x-[x])$ is

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Understanding +4 | -1

The Domain of function

f(x)=\log _e(x-[x])

View answer and explanation

Correct option: A

\mathrm{R}

Option C (

(0,+\infty)

) is the correct domain because the argument of the logarithm,

x-[x]

, must be greater than 0, and

x-[x]

represents the fractional part of x, which is always in the interval [0, 1). Since the log is undefined at 0, the domain is (0, +∞).

Practice All Chapter MCQs →

f:(-\infty, 2] \longrightarrow(-\infty, 4]

f(x)=x(4-x)

f^{-1}(x)

g(f(x))=|\sin x|

f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

S=\left\{x: f(x)=f^{-1}(x)\right\}