Natural domain of a function of one variable

$y=\log (x^{2}-4)$;

$y=\log (x+2)+\log (x-2)$.

$f(\sin x)$;

$f(\ln x)$;

$f\left(\dfrac {[x]}{x}\right)$.

$y = \frac{x}{x+1}$

$y = \frac{x+1}{x^{2}-1}$

$y = \frac{x^{3}-1}{x^{2}-6 x+8}$

$y = \frac{(x+2)^{2}}{x^{3}-4 x}$

$y = \frac{1}{x+\left|x\right|}$;

$y = \frac{x^{2}}{2\left|x\right|-3}$;

$y = \frac{\left|x+2\right|+1-2 x-2 x^{2}}{\left|2 x+2\right|-1}$.

$y = \sqrt[3]{x^{2}-1}$;

$y = \sqrt{-x^{2}}$

$y = \sqrt[4]{2-x}$

$y = \sqrt{2-x-x^{2}}$

$y = \frac{1}{\sqrt{1-x^{2}}}$;

$y = \frac{\sqrt[6]{x^{2}-1}}{x}$;

$y = \frac{x}{\left(9-x^{2}\right)^{2 / 3}}$;

$y = \sqrt{x^{2}(x-2)}$;

$y = \sqrt{\frac{x-3}{1-3 x+2 x^{2}}}$.

$f_{1}(x) = \sqrt[4]{3-x}, f_{2}(x) = \sqrt{x+1}$;

$f_{1}(x) = \sqrt{1-x^{2}}, f_{2}(x) = \sqrt[3]{\frac{x}{2 x-1}}$

$f_{1}(x) = \sqrt{x}-\sqrt{x-3}, f_{2}(x) = \lg \left(x^{2}-4\right)$;

$f_{1}(x) = \frac{1}{\sqrt[4]{5 x-x^{2}}}, f_{2}(x) = \operatorname {tg}(x)$;

$f_{1}(x) = \lg \left(16-x^{2}\right), f_{2}(x) = \frac{1}{1-\sin x}$;

$f_{1}(x) = x+\sqrt{x-1}, f_{2}(x) = x-\sqrt{x-1}$.

$f(x) = x^{2}-x+1$

$f(x) = \left|x\right|-2$

$f(x) = \lg \left(1-x^{2}\right)$;

$f(x) = x+\sqrt{x+2}$

$f(x) = \sqrt{2 x+1}-\sqrt{x+1}$

$f(x) = 5^{x}-2^{x+1}$

$f(x) = 3-2 \cos x$

$f(x) = \sqrt{2}-2 \sin x$

$f(x) = 1-\operatorname {ctg} x$.

$f(x) = x^{2}, g(x) = \sqrt{x}$

$f(x) = g(x) = \sqrt{1-x^{2}}$;

$f(x) = 10^{x}, g(x) = \lg x$

$f(x) = x^{5}, g(x) = x+5$;

$f(x) = \begin{cases} x, & x \in [0 ;+\infty ) \\ 0, & x \in (-\infty ; 0)\end{cases}$, $g(x) = \begin{cases} 0, & x \in [0 ;+\infty ), \\ x^{2}, & x \in (-\infty ; 0) ; \end{cases}$

$f(x) = \ln x^{2}, g(x) = \sin x$.

$y = \frac{1}{16^{x^{2}}-2^{x}}$

$y = \sqrt{2^{x}-3^{x}}$

$y = \log_{2} x^{2}$ and $y = 2 \log_{2} x$;

$y = \log_{x} 5$;

$y = (\lg (100-x))^{-1}$;

$y = \ln x+\ln (x-1)$ and $y = \ln x(x-1)$;

$y = \log_{3+x}\left(x^{2}-1\right)$;

$y = \log_{3} \log_{0,5} x$.

$y = \sqrt{\frac{x}{6-x}}$;

$y = \sqrt{3-5 x-2 x^{2}}$;

$y = \sqrt[3]{\frac{x}{1-\left|x\right|}}$;

$y = \sqrt{x^{2}-\left|x\right|-2}$

$y = \sqrt[4]{3+x}+\sqrt[4]{3-x}$

$y = \left(8-2 x-x^{2}\right)^{-3 / 2}$.

$y = \lg \left(x^{2}+1\right)$;

$y = \sqrt[3]{\frac{x+2}{\lg \cos x}}$;

$y = \lg \frac{3 x-x^{2}}{x-1}$

$y = \sqrt{\log_{3} \frac{2 x-3}{x-1}}$;

$y = \frac{\sqrt{x+5}}{\lg (9-5 x)}$;

$y = \frac{\sqrt{x^{2}-4}}{\log_{2}\left(x^{2}+2 x-3\right)}$;

$y = \log_{x+1}\left(x^{2}-3 x+2\right)$;

$y = \log_{x} \log_{0,5}\left(\frac{4}{3}-2^{x-1}\right)$;

$y = \lg \left(1,25^{1-x^{2}}-0,4096^{1+x}\right)$;

$y = \ln \left(1-\lg \left(x^{2}-5 x+16\right)\right)$.