18. $$ h(8)-2 \cdot f(3) $$ $$ h(x)=-x-7 $$ $$ f(x)=-x^{2}+8 x-11 $$

Question

UpStudy AI · Accepted Answer

Evaluate the expression by following steps:
- step0: Evaluate:
  $$-x-7$$
- step1: Substitute:
  $$-8-7$$
- step2: Subtract the numbers:
  $$-15$$
Substitute $$ x=3 $$ into the expression $$ -x^{2}+8 x-11 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$-x^{2}+8x-11$$
- step1: Substitute:
  $$-3^{2}+8\times 3-11$$
- step2: Multiply the numbers:
  $$-3^{2}+24-11$$
- step3: Evaluate the power:
  $$-9+24-11$$
- step4: Calculate:
  $$4$$
Let's solve the expression $$ h(8) - 2 \cdot f(3) $$ step by step.

1. **Calculate $$ h(8) $$**:
   - The function is given as $$ h(x) = -x - 7 $$.
   - Substituting $$ x = 8 $$:
     $$
     h(8) = -8 - 7 = -15
     $$

2. **Calculate $$ f(3) $$**:
   - The function is given as $$ f(x) = -x^2 + 8x - 11 $$.
   - Substituting $$ x = 3 $$:
     $$
     f(3) = -3^2 + 8 \cdot 3 - 11 = -9 + 24 - 11 = 4
     $$

3. **Combine the results**:
   - Now we substitute these values into the expression:
     $$
     h(8) - 2 \cdot f(3) = -15 - 2 \cdot 4
     $$
   - Calculate $$ 2 \cdot 4 = 8 $$:
     $$
     -15 - 8 = -23
     $$

Thus, the final result is:
$$
\boxed{-23}
$$
The result of $$ h(8) - 2 \cdot f(3) $$ is -23.

18. \( h(8)-2 \cdot f(3) \) \( h(x)=-x-7 \) \( f(x)=-x^{2}+8 x-11 \)

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