Question

The domain of the function $f\left(x\right)=2^{{\log }_{2}x}+\frac{2x+3}{x^2-4x+3}$ is

• A. $R-\{1,3\}$
• B. $R-\left\{1\right\}$
• C. $R-\left\{3\right\}$
• D. $(0,\infty )-\{1,3\}$

Answer 1

The correct option is D $(0,\infty )-\{1,3\}$

For $f$ to be defined,
$x>0$ and $x^2-4x+3\ne 0$
$\Rightarrow x>0$ and $(x-1)(x-3)\ne 0$
$\Rightarrow x>0$ and $x\ne 1,3$
i.e., $x\in (0,\infty )-\{1,3\}$