Verified answer

[tex]y = \sqrt{x - 1} + \frac{3}{x - 5} \\ \displaystyle\bf\\\left \{ {{x - 1 \geqslant 0} \atop {x - 5\neq0 }} \right. \\ \displaystyle\bf\\\left \{ {{x \geqslant 1} \atop {x\neq5 }} \right. \\ \\ otvet \: \: \: x \: \epsilon\: [1; \: 5)U(5; \: + \propto)[/tex]