$$ \quad y = \pi ^{\sqrt {\frac{{x - 2}}{{5 - 2x}}} } + \sin x$$

$$ \quad D(f):\frac{{x - 2}}{{5 - 2x}} \ge 0$$

$$ \quad$$ $$ y = \sqrt {f(x)}$$

$$ \quad$$ $$D\left( {\sqrt {f(x)} } \right):f(x) \ge 0$$

$$ \quad$$ $$y = \cos \left( {\frac{2}{{3 - x}} - 7} \right)$$

$$ \quad$$ $$D(f):3 - x \ne 0$$

$$ \quad$$ $$y = \frac{1}{{f(x)}}$$

$$ \quad$$ $$D\left( {\frac{1}{{f(x)}}} \right):f(x) \ne 0$$

$$ \quad$$ $$y = e^{\log _3 \left( {4x^2 - 5x} \right)} $$

$$ \quad$$ $$D(f):4x^2 - 5x > 0$$

$$ \quad$$ $$ y = \log _a f(x)$$

$$ \quad$$ $$ D\left( {\log _a f(x)} \right):f(x) > 0$$

$$ \quad$$ $$y = \sin \left( {\log _{4x^2 + 3x} 3} \right)$$

$$ \quad$$ $$D(f):\left\{ \begin{array}{l} 4x^2 + 3x > 0, \\ 4x^2 + 3x \ne 1. \\ \end{array} \right.$$

$$ \quad$$ $$ y = \log _{f(x)} a $$

$$ \quad$$ $$ D\left( {\log _{f(x)} a} \right):\left\{ \begin{array}{l} f(x) > 0, \\ f(x) \ne 0. \\ \end{array} \right.$$

$$ \quad$$ $$y = tg\left( {x + \frac{\pi }{3}} \right) - \sin \left( {2x^2 - \frac{{2\pi }}{3}} \right)$$

$$ \quad$$ $$D(f):x + \frac{\pi }{3} \ne \frac{\pi }{2} + \pi n,n \in Z$$

$$ \quad$$ $$ y = tg\,f(x)$$

$$ \quad$$ $$D(tg\,f(x)):f(x) \ne \frac{\pi }{2} + \pi n,n \in Z$$

$$ \quad$$ $$y = \arccos \left( {5^{2x - 1} + x^2 } \right)$$

$$ \quad$$ $$D(f): - 1 \le 5^{2x - 1} + x^2 \le 1$$

$$ \quad$$ $$ \begin{array}{l} y = \arccos f(x) \\ y = \arcsin f(x) \\ \end{array}$$

$$ \quad$$ $$ D\left( {\left[ \begin{array}{l} \arccos f(x) \\ \arcsin f(x) \\ \end{array} \right.} \right): - 1 \le f(x) \le 1$$