Задача 43520 ...

vk539410681

2020-01-20 06:55:03

u(x) = {tgx, x < 0, lnx, x ≥ 0}

v(x) = 1/x

f(x) = u(v(x)) = ?
g(g) = v(u(x)) = ?

sova

2020-01-20 10:54:17

★

[m]x\overset{v}{\rightarrow}\frac{1}{x}[/m]

[m]x\overset{u}{\rightarrow}\left\{\begin{matrix} tgx, x <0\\ lnx, x \geq 0 \end{matrix}\right.[/m]

поэтому сложная функция u(v(x)):

[m]x\overset{v}{\rightarrow}\frac{1}{x}\overset{u}{\rightarrow}\left\{\begin{matrix} tg\frac{1}{x}, x <0\\ ln\frac{1}{x}, x \geq 0 \end{matrix}\right.[/m]

f(x)=u(v(x))=[m]\left\{\begin{matrix} tg\frac{1}{x}, x <0\\ ln\frac{1}{x}, x \geq 0 \end{matrix}\right.[/m]

a сложная функция v(u(x)):

[m]x\overset{u}{\rightarrow}\left\{\begin{matrix} tgx, x <0\\ lnx, x \geq 0 \end{matrix}\right.\overset{v}{\rightarrow}\left\{\begin{matrix}\frac{1}{tgx}, x <0\\ \frac{1}{lnx}, x \geq 0 \end{matrix}\right.[/m]

g(x)=v(u(x))=[m]\left\{\begin{matrix} \frac{1}{tgx}, x <0\\ \frac{1}{lnx}, x \geq 0 \end{matrix}\right.[/m]