Question

The domain of $f\left(x\right)=\sqrt{x-2}+\frac{1}{\log (4-x)}$ is

• A. $[2,\infty )$
• B. $(-\infty ,4)$
• C. $[2,3)\cup (3,4)$
• D. $[3,\infty )$

Answer 1

Answer: (C)

$[2,3)\cup (3,4)$

To find Domain of
$f\left(x\right)=\sqrt{x-2}+\frac{1}{log(4-x)}$
For the domain of f(x) to be defined , we have
$x-2\ge 0$
$x\ge 2$
$log(4-x)\ne 0$
For log to be defined , we have
$4-x>0$
$4>x$
Hence, Domain of the function f(x) defined as
$x\in [2,3)\cup (3,4)$