Question

The domain of the function $f\left(x\right)=\frac{4}{\{x-4\}}$ is
(where $\{.\}$ denotes the fractional part of $x$)

• A. $Z-\left\{4\right\}$
• B. $R$
• C. $R-\left\{4\right\}$
• D. $R-Z$

Answer 1

The correct option is D $R-Z$

$f\left(x\right)=\frac{4}{\{x-4\}}$
For the function to be defined, we get
$\{x-4\}\ne 0\Rightarrow \left\{x\right\}\ne 0(\because \{x-Z\}=\{x\left\}\right)\Rightarrow x\notin Z$
$\therefore D_f=R-Z$