Question

$y=\frac{1}{\sqrt{4x-|x^2-10x+9}|}$, find the domain of the function.

Answer 1

$4x-|x^2-10x+9|>0$

$4x>|x^2-10x+9|$

$-4x<x^2-10x+9<4x$

$x^2-6x+9>0$ and $x^2-14x+9<0$

$(x-3{)}^2>0$ and $(x-7+2\sqrt{10})(x+7-2\sqrt{10})<0$

$x>3$ and $0.6754<x<13.324$

or, $3<x<13.324$