Find the inverse of each function \( \begin{array}{lll}\text { a } f(x)=7 x & \text { b } f(x)=\frac{1}{7 x^{3}} & \text { c } f(x)=x^{3} \\ \text { d } f(x)=4 x+3 & \text { e } f(x)=\frac{1}{2} x+5 & \text { \& } f(x)=\frac{x+2}{2} \\ \text { g } f(x)=3(x-2) & \text { h } f(x)=\frac{2 x+9}{2} & \text { i } f(x)=\frac{2(x+1)}{4-x} \\ \text { f } f(x)=x^{3}+5 & \text { k } f(x)=\sqrt{3 x+8} & \text { l } f(x)=\frac{x+1}{x-1}\end{array} \)

Here are the inverses of the given functions: a. \( f(x) = 7x \) Inverse: \( f^{-1}(x) = \frac{x}{7} \) b. \( f(x) = \frac{1}{7x^{3}} \) Inverse: \( f^{-1}(x) = \frac{\sqrt[3]{49x^{2}}}{7x} \) c. \( f(x) = x^{3} \) Inverse: \( f^{-1}(x) = \sqrt[3]{x} \) d. \( f(x) = 4x + 3 \) Inverse: \( f^{-1}(x) = \frac{x - 3}{4} \) e. \( f(x) = \frac{1}{2}x + 5 \) Inverse: \( f^{-1}(x) = 2x - 10 \) f. \( f(x) = \frac{x + 2}{2} \) Inverse: \( f^{-1}(x) = 2x - 2 \) g. \( f(x) = 3(x - 2) \) Inverse: \( f^{-1}(x) = \frac{x + 6}{3} \) h. \( f(x) = \frac{2x + 9}{2} \) Inverse: \( f^{-1}(x) = \frac{2x - 9}{2} \) i. \( f(x) = \frac{2(x + 1)}{4 - x} \) Inverse: \( f^{-1}(x) = \frac{-2 + 4x}{2 + x} \) j. \( f(x) = x^{3} + 5 \) Inverse: \( f^{-1}(x) = \sqrt[3]{x - 5} \) k. \( f(x) = \sqrt{3x + 8} \) Inverse: \( f^{-1}(x) = \frac{x^{2} - 8}{3} \) l. \( f(x) = \frac{x + 1}{x - 1} \) Inverse: \( f^{-1}(x) = -\frac{x + 1}{1 - x} \) These inverses allow you to find the original input \( x \) given the output \( f(x) \).