第1章 1.4

(1)

$y = 3x - 2$

$3x = y + 2$

$x = \frac{1}{3}(y + 2)$

x と y を入れ換えて

$y = \frac{1}{3}(x + 2)$

(2)

$y = 1 - x^2 \quad (x \geq 0)$

$x^2 = 1 - y$

$x = \sqrt{1 - y}$

x と y を入れ換えて

$y = \sqrt{1 - x}$

(3)

$y = \frac{1}{2x + 5}$

$2x + 5 = \frac{1}{y}$

$x = \frac{1}{2}\left(\frac{1}{y} - 5\right) = \frac{1 - 5y}{2y}$

x と y を入れ換えて

$y = \frac{1 - 5x}{2x}$

(4)

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

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

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

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

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

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

x と y を入れ換えて

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

(5)

$y = e^{x-1}$

$\log y = \log e^{x-1} = x-1$

$x = \log y + 1$

x と y を入れ換えて

$y = \log x + 1$

(6)

$y = \log(x-1)$

$e^y = e^{\log(x-1)}$

$e^y = x-1$

$x = e^y + 1$

$x$ と $y$ を入れ換えて

$y = e^x + 1$