1. [tex]h(x) = \sqrt[3]{x} - 3[/tex]
[tex]y = \sqrt[3]{x} - 3[/tex]
[tex]x = \sqrt[3]{y} - 3[/tex]
[tex]x + 3 = \sqrt[3]{y}[/tex]
[tex](x + 3)^{3} = y[/tex]
[tex](x + 3)(x + 3)(x + 3) = y[/tex]
[tex](x(x + 3) + 3(x + 3))(x + 3) = y[/tex]
[tex](x(x) + x(3) + 3(x) + 3(3))(x + 3) = y[/tex]
[tex](x^{2} + 3x + 3x + 9)(x + 3) = y[/tex]
[tex](x^{2} + 6x + 9)(x + 3) = y[/tex]
[tex]x^{2}(x + 3) + 6x(x + 3) + 9(x + 3) = y[/tex]
[tex]x^{2}(x) + x^{2}(3) + 6x(x) + 6x(3) + 9(x) + 9(3) = y[/tex]
[tex]x^{3} + 3x^{2} + 6x^{2} + 18x + 9x + 27 = y[/tex]
[tex]x^{3} + 9x^{2} + 27x + 27 = y[/tex]
[tex]x^{3} + 9x^{2} + 27x + 27 = h^{-1}(x)[/tex]
2. [tex]g(x) = \frac{1}{x} - 2x[/tex]
[tex]y = \frac{1}{x} - 2y[/tex]
[tex]x = \frac{1}{x} - 2y[/tex]
[tex]x - \frac{1}{x} = -2y[/tex]
[tex]\frac{x - \frac{1}{x}}{-2} = \frac{-2y}{-2}[/tex]
[tex]-\frac{1}{2}x + \frac{1}{2x} = y[/tex]
[tex]-\frac{1}{2}x + \frac{1}{2x} = g^{-1}(x)[/tex]
3. [tex]f(x) = 4x[/tex]
[tex]y = 4x[/tex]
[tex]x = 4y[/tex]
[tex]\frac{x}{4} = \frac{4y}{4}[/tex]
[tex]\frac{1}{4}x = y[/tex]
[tex]\frac{1}{4}x = f^{-1}(x)[/tex]
4. [tex]f(x) = -\frac{1}{5}x - 1[/tex]
[tex]y = -\frac{1}{5}x - 1[/tex]
[tex]x = -\frac{1}{5}y - 1[/tex]
[tex]x + 1 = -\frac{1}{5}y[/tex]
[tex]-5(x + 1) = -5(-\frac{1}{5}y)[/tex]
[tex]-5(x) - 5(1) = y[/tex]
[tex]-5x - 5 = y[/tex]
[tex]-5x - 5 = f^{-1}(x)[/tex]
5. [tex]g(x) = \frac{1}{x - 1}[/tex]
[tex]y = \frac{1}{x - 1}[/tex]
[tex]y(x - 1) = x - 1(\frac{1}{x - 1})[/tex]
[tex]y(x) - y(1) = -1[/tex]
[tex]xy - y = -1[/tex]
[tex]xy = y - 1[/tex]
[tex]\frac{xy}{y} = \frac{y - 1}{y}[/tex]
[tex]x = 1 - \frac{1}{y}[/tex]
[tex]y = 1 - \frac{1}{x}[/tex]
[tex]f^{-1}(x) = 1 - \frac{1}{x}[/tex]
6. [tex]f(x) = -2x^{3} + 1[/tex]
[tex]y = -2x^{3} + 1[/tex]
[tex]x = -2y^{3} + 1[/tex]
[tex]x - 1 = -2y^{3}[/tex]
[tex]\frac{x - 1}{-2} = \frac{-2y^{3}}{-2}[/tex]
[tex]-\frac{1}{2}x + \frac{1}{2} = y^{3}[/tex]
[tex]\sqrt[3]{-\frac{1}{2}x + \frac{1}{2}} = y[/tex]
[tex]\sqrt[3]{-\frac{1}{2}x + \frac{1}{2}} = f^{-1}(x)[/tex]
7. [tex]g(x) = \frac{-x - 5}{3}[/tex]
[tex]y = \frac{-x - 5}{3}[/tex]
[tex]y(3) = 3(\frac{-x - 5}{3})[/tex]
[tex]3y = -x - 5[/tex]
[tex]3x + 5 = -y[/tex]
[tex]\frac{3x + 5}{-1} = \frac{-y}{-1}[/tex]
[tex]-3x - 5 = y[/tex]
[tex]-3x - 5 = f^{-1}(x)[/tex]
