For each function below, find \( f^{-1}(x) \) \( \begin{array}{ll}\text { 13. } f(x)=x+3 & \text { 14. } f(x)=x+5 \\ \text { 15. } f(x)=2-x & \text { 16. } f(x)=3-x \\ \text { 17. } f(x)=11 x+7 & \text { 18. } f(x)=9+10 x\end{array} \)

To find the inverse functions for each of the functions provided, we will follow these steps: replace \( f(x) \) with \( y \), swap \( x \) and \( y \), and then solve for \( y \). 1. **For \( f(x) = x + 3 \)**: - Set \( y = x + 3 \) - Swap: \( x = y + 3 \) - Solve for \( y \): \( y = x - 3 \) - Thus, \( f^{-1}(x) = x - 3 \) 2. **For \( f(x) = x + 5 \)**: - Set \( y = x + 5 \) - Swap: \( x = y + 5 \) - Solve for \( y \): \( y = x - 5 \) - Thus, \( f^{-1}(x) = x - 5 \) 3. **For \( f(x) = 2 - x \)**: - Set \( y = 2 - x \) - Swap: \( x = 2 - y \) - Solve for \( y \): \( y = 2 - x \) - Thus, \( f^{-1}(x) = 2 - x \) 4. **For \( f(x) = 3 - x \)**: - Set \( y = 3 - x \) - Swap: \( x = 3 - y \) - Solve for \( y \): \( y = 3 - x \) - Thus, \( f^{-1}(x) = 3 - x \) 5. **For \( f(x) = 11x + 7 \)**: - Set \( y = 11x + 7 \) - Swap: \( x = 11y + 7 \) - Solve for \( y \): \( y = \frac{x - 7}{11} \) - Thus, \( f^{-1}(x) = \frac{x - 7}{11} \) 6. **For \( f(x) = 9 + 10x \)**: - Set \( y = 9 + 10x \) - Swap: \( x = 9 + 10y \) - Solve for \( y \): \( y = \frac{x - 9}{10} \) - Thus, \( f^{-1}(x) = \frac{x - 9}{10} \) So, the final inverses are: - \( f^{-1}(x) = x - 3 \) for \( f(x) = x + 3 \) - \( f^{-1}(x) = x - 5 \) for \( f(x) = x + 5 \) - \( f^{-1}(x) = 2 - x \) for \( f(x) = 2 - x \) - \( f^{-1}(x) = 3 - x \) for \( f(x) = 3 - x \) - \( f^{-1}(x) = \frac{x - 7}{11} \) for \( f(x) = 11x + 7 \) - \( f^{-1}(x) = \frac{x - 9}{10} \) for \( f(x) = 9 + 10x \)