Use the following function rule to find f(–9).

Question

f(x) =
7
x
+
2
x
2

+ 2

f(–9) =

Answer 1

To find \( f(-9) \) using the given function rule \( f(x) = 7x + 2x^2 + 2 \), we need to substitute \( x = -9 \) into the function.

Let's compute it step by step:

1. Substitute \( x = -9 \) into the function: \[ f(-9) = 7(-9) + 2(-9)^2 + 2 \]

2. Calculate \( 7(-9) \): \[ 7(-9) = -63 \]

3. Calculate \( 2(-9)^2 \): \[ (-9)^2 = 81 \quad \text{so} \quad 2(-9)^2 = 2 \times 81 = 162 \]

4. Now, combine all the parts together: \[ f(-9) = -63 + 162 + 2 \]

5. Simplify the expression: \[ -63 + 162 = 99 \] \[ 99 + 2 = 101 \]

Thus, \( f(-9) = 101 \).