Question

Given f, of, x, equals, minus, x, squared, plus, 18f(x)=−x
2
+18, find f, of, minus, 2f(−2)

Answer 1

To find \( f(-2) \) using the given function \( f(x) = -x^2 + 18 \), we can substitute \(-2\) into the function:

\[
f(-2) = -(-2)^2 + 18
\]

Calculating \((-2)^2\):

\[
(-2)^2 = 4
\]

So,

\[
f(-2) = -4 + 18 = 14
\]

Next, we need to find \( f(-2) \) again, which we have already calculated as 14. Thus, we are looking for \( f(f(-2)) = f(14) \).

Now, we find \( f(14) \):

\[
f(14) = -14^2 + 18
\]

Calculating \( 14^2 \):

\[
14^2 = 196
\]

So,

\[
f(14) = -196 + 18 = -178
\]

Therefore, the final answer is:

\[
f(f(-2)) = -178
\]

Thus, \( f(-2) \) evaluates to \(-178\).