Question

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

• A. $\varphi$
• B. $R-\left\{0\right\}$
• C. $R^{-}$
• D. $N$

Answer 1

The correct option is C $R^{-}$

For $f$ to be defined,
$\frac{2^x+3^x}{2^x-3^x}\ge 0$
$\Rightarrow 2^x-3^x>0$
$\Rightarrow 2^x>3^x$
$\Rightarrow {\left(\frac{3}{2}\right)}^x<1$
$\Rightarrow x<0$