Evaluate the function \( f(x)=7 x+9 \) at the given values of the independent variable and simplify. \( \begin{array}{lll}\text { a. } f(6) & \text { b. } f(x+2) & \text { c. } f(-x)\end{array} \)

Let's evaluate the function \( f(x) = 7x + 9 \) for each of the given inputs. ### a. \( f(6) \) To find \( f(6) \), substitute \( x \) with 6: \[ f(6) = 7(6) + 9 = 42 + 9 = 51 \] **Answer:** \( f(6) = 51 \) --- ### b. \( f(x + 2) \) To find \( f(x + 2) \), substitute \( x \) with \( x + 2 \): \[ f(x + 2) = 7(x + 2) + 9 \] Now, distribute the 7: \[ f(x + 2) = 7x + 14 + 9 \] Combine like terms: \[ f(x + 2) = 7x + 23 \] **Answer:** \( f(x + 2) = 7x + 23 \) --- ### c. \( f(-x) \) To find \( f(-x) \), substitute \( x \) with \( -x \): \[ f(-x) = 7(-x) + 9 \] Simplify the expression: \[ f(-x) = -7x + 9 \] **Answer:** \( f(-x) = -7x + 9 \) --- Feel free to ask if you have any more questions!