Question

Find the domain of definition of the following function:
$y=\sqrt{x-4}-\frac{x}{x-5}+\log (39-x).$

Answer 1

$x-4\ge 0x\ge 4$

$\frac{x}{x-5}x\ne 5$

$\log (39-x)39-x>039>x$

Taking intersection, we get

$x\in [4,39)-\left\{5\right\}$