Question

Find the domain of $f\left(x\right)=\frac{1}{\sqrt{lo{g}_{1/2}(x^2-7x+13)}}$

Answer 1

$f\left(x\right)=\frac{1}{\sqrt{{\log }_{\frac{1}{2}}(x^2-7x+13)}}$

${\log }_{\frac{1}{2}}(x^2-7x+13)>0$ $(\ne 0b<zdenominator)$

$x^2-7x+13>1\Rightarrow x^2-7x+12>0$

$(x-4)(x-3)>0$

$x\in (-10,3)(4,10)$