Question

Function $f\left(x\right)=\frac{1}{\left[3x\right]-1}$ is defined for

• A. $xϵR$
• B. $xϵR\sim \left(\frac{1}{3}\right)$
• C. $xϵR\sim \left(\frac{2}{3}\right)$
• D. None of these

Answer 1

Answer: (D)

None of these

$f\left(x\right)=\frac{1}{\left[3x\right]-1}$

The above function is defined for-

$\left[3x\right]-1\ne 0$

$\left[3x\right]\ne 1$

Therefore,

$x\in R-[\frac{1}{3},\frac{2}{3}]$

Thus the function $f\left(x\right)$ is defined for $x\in R-[\frac{1}{3},\frac{2}{3}]$.

Hence $\left(D\right)$ will be correct answer.