Question

Given f, of, x, equals, minus, 2, x, squared, plus, 2f(x)=−2x
2
+2, find f, of, minus, 6f(−6)

Answer 1

To find \( f(-6) \) from the function \( f(x) = -2x^2 + 2 \), we will follow these steps:

1. **Substitute \(-6\) into the function \( f(x) \)**:

\[
f(-6) = -2(-6)^2 + 2
\]

2. **Calculate \((-6)^2\)**:

\[
(-6)^2 = 36
\]

3. **Substitute \(36\) back into the function**:

\[
f(-6) = -2 \cdot 36 + 2
\]

4. **Calculate \(-2 \cdot 36\)**:

\[
-2 \cdot 36 = -72
\]

5. **Add \(2\)**:

\[
f(-6) = -72 + 2 = -70
\]

So, \( f(-6) = -70 \).

Thus, the final answer is:

\[
f(-6) = -70
\]