Given f, of, x, equals, minus, x, squared, minus, 8, x, plus, 8f(x)=−x

Question

2
−8x+8, find f, of, minus, 5f(−5)

Answer 1

To find \( f(-5) \) for the function

\[ f(x) = -x^2 - 8x + 8, \]

we substitute \(-5\) for \(x\):

\[ f(-5) = -(-5)^2 - 8(-5) + 8. \]

Calculating each term:

1. \(-(-5)^2 = -25\),
2. \(-8(-5) = 40\),
3. \(+8\).

Now putting it all together:

\[ f(-5) = -25 + 40 + 8. \]

Calculating this step-by-step:

1. \(-25 + 40 = 15\),
2. \(15 + 8 = 23\).

Thus,

\[ f(-5) = 23. \]

So, the final answer is:

\[ \boxed{23}. \]