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

Below is the step‐by‐step process to find the inverse function \( f^{-1}(x) \) for each given function. --- ### 13. \( f(x)=x+3 \) 1. Write the function as: \[ y = x+3. \] 2. Swap \( x \) and \( y \): \[ x = y+3. \] 3. Solve for \( y \): \[ y = x-3. \] Thus, the inverse function is: \[ f^{-1}(x)=x-3. \] --- ### 14. \( f(x)=x+5 \) 1. Write the function as: \[ y = x+5. \] 2. Swap \( x \) and \( y \): \[ x = y+5. \] 3. Solve for \( y \): \[ y = x-5. \] Thus, the inverse function is: \[ f^{-1}(x)=x-5. \] --- ### 15. \( f(x)=2-x \) 1. Write the function as: \[ y = 2-x. \] 2. Swap \( x \) and \( y \): \[ x = 2-y. \] 3. Solve for \( y \): \[ y = 2-x. \] Thus, the inverse function is: \[ f^{-1}(x)=2-x. \] --- ### 16. \( f(x)=3-x \) 1. Write the function as: \[ y = 3-x. \] 2. Swap \( x \) and \( y \): \[ x = 3-y. \] 3. Solve for \( y \): \[ y = 3-x. \] Thus, the inverse function is: \[ f^{-1}(x)=3-x. \] --- ### 17. \( f(x)=11x+7 \) 1. Write the function as: \[ y = 11x+7. \] 2. Swap \( x \) and \( y \): \[ x = 11y+7. \] 3. Isolate the term with \( y \): \[ 11y = x-7. \] 4. Solve for \( y \): \[ y = \frac{x-7}{11}. \] Thus, the inverse function is: \[ f^{-1}(x)=\frac{x-7}{11}. \] --- ### 18. \( f(x)=9+10x \) 1. Write the function as: \[ y = 9+10x. \] 2. Swap \( x \) and \( y \): \[ x = 9+10y. \] 3. Isolate the term with \( y \): \[ 10y = x-9. \] 4. Solve for \( y \): \[ y = \frac{x-9}{10}. \] Thus, the inverse function is: \[ f^{-1}(x)=\frac{x-9}{10}. \] --- Each function’s inverse was determined by swapping \( x \) and \( y \) and then solving for \( y \).