Question

помогите найти область определения функции​

Answer 1

$D_1(f(x))=x^2-5x+1\geq 0\Leftrightarrow \cfrac{1}{4}\left (4x^2-20x+25 \right )-\cfrac{21}{4}\geq 0\Leftrightarrow \cfrac{1}{4}(2x-5)^2-\cfrac{21}{4}\geq 0$$(2x-5)^2\geq 21\Rightarrow x\in \left (-\infty ,\cfrac{5-\sqrt{21}}{2} \right ]\cup \left [ \cfrac{5+\sqrt{21}}{2},\infty \right ]$

$D_2(f(x))=\begin{cases}x-4 > 0\\ \ln(x-4)\neq 0\end{cases}\Rightarrow \begin{cases}x > 4\\ x-4\neq 1\end{cases}\Rightarrow \begin{cases}x > 4\\ x\neq 5\end{cases}\Rightarrow x\in (4,\infty )\setminus \left \{ 5 \right \}$