Question

Given f, of, x, equals, minus, x, squared, minus, 5, x, minus, 9f(x)=−x
2
−5x−9, find f, of, minus, 9f(−9)

Answer 1

To find \( f(-9) \) for the function \( f(x) = -x^2 - 5x - 9 \), we will substitute \( -9 \) into the function.

Here's the calculation step by step:

1. Substitute \( -9 \) for \( x \) in the function:
\[
f(-9) = -(-9)^2 - 5(-9) - 9
\]

2. Calculate \( (-9)^2 \):
\[
(-9)^2 = 81
\]

3. Substitute this value back into the equation:
\[
f(-9) = -81 - 5(-9) - 9
\]

4. Calculate \( 5 \times (-9) \):
\[
5(-9) = -45
\]

5. Now substitute back into the equation:
\[
f(-9) = -81 + 45 - 9
\]

6. Simplify:
\[
f(-9) = -81 + 45 = -36
\]
\[
-36 - 9 = -45
\]

Thus, \( f(-9) = -45 \).

The final answer is:
\[
f(-9) = -45
\]