Question

if f(x)=-x-11 ; find the following
1) 4f(-2)+5f(1) 2) 3f(5)xf(2)
3) -5f(12)-2f(-9) 4) f(9)/f(-6)

Answer 1

To solve the problem, we first need to compute the function \( f(x) = -x - 11 \) for the specific values given.

1. **Calculating \( f(-2) \) and \( f(1) \)**:
- \( f(-2) = -(-2) - 11 = 2 - 11 = -9 \)
- \( f(1) = -(1) - 11 = -1 - 11 = -12 \)

Now, substitute these values into the expression:
\[
4f(-2) + 5f(1) = 4(-9) + 5(-12) = -36 - 60 = -96
\]

2. **Calculating \( f(5) \) and \( f(2) \)**:
- \( f(5) = -(5) - 11 = -5 - 11 = -16 \)
- \( f(2) = -(2) - 11 = -2 - 11 = -13 \)

Now calculate:
\[
3f(5) \times f(2) = 3(-16) \times (-13) = -48 \times -13 = 624
\]

3. **Calculating \( f(12) \) and \( f(-9) \)**:
- \( f(12) = -(12) - 11 = -12 - 11 = -23 \)
- \( f(-9) = -(-9) - 11 = 9 - 11 = -2 \)

Now calculate:
\[
-5f(12) - 2f(-9) = -5(-23) - 2(-2) = 115 + 4 = 119
\]

4. **Calculating \( f(9) \) and \( f(-6) \)**:
- \( f(9) = -(9) - 11 = -9 - 11 = -20 \)
- \( f(-6) = -(-6) - 11 = 6 - 11 = -5 \)

Now calculate:
\[
\frac{f(9)}{f(-6)} = \frac{-20}{-5} = 4
\]

Putting it all together, we have the results:

1) \( 4f(-2) + 5f(1) = -96 \)

2) \( 3f(5) \times f(2) = 624 \)

3) \( -5f(12) - 2f(-9) = 119 \)

4) \( \frac{f(9)}{f(-6)} = 4 \)