Question

Помогите пожалуйста, с подробным решением.
Найти область определения функции

Answer 1

$f(x) = arcsin\frac{x-3}{2} -lg\frac{x-1}{x^3+3x^2+x+3}\\\left \{ {{-1\leq \frac{x-3}{2} \leq 1 } \atop {\frac{x-1}{x^3+3x^2+x+3} > 0}} \right. => \left \{ {{-2 \leq x-3 \leq 2 } \atop {\frac{x-1}{x^3+3x^2+3x+1 + 2x + 2}> 0}} \right. => \left \{ {{1 \leq x \leq 5} \atop {\frac{x-1}{(x+1)^3+2(x+1)}}>0} \right. => \left \{ {{1\leq x\leq5 } \atop {\frac{x-1}{(x+1)((x+1)^2+2)}>0}} \right. => \left \{ {{1\leq x\leq5} \atop {\frac{x-1}{x+1}>0} \right. =>$$=> \left \{ {{1\leq x \leq 5 } \atop {x = (-\infty; -1)(1; +\infty)}} \right. => x = (1; 5]\\ Answer: x = (1; 5]$