Questions: g(n)=-2 n-2 h(n)=n^2+5 n Find (5 g-4 h)(-2)

g(n)=-2 n-2 h(n)=n^2+5 n Find (5 g-4 h)(-2)
Transcript text: $\begin{array}{l}g(n)=-2 n-2 \\ h(n)=n^{2}+5 n \\ \text { Find }(5 g-4 h)(-2)\end{array}$
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Solution

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Solution Steps

To solve the given problem, we need to:

  1. Evaluate the functions \( g(n) \) and \( h(n) \) at \( n = -2 \).
  2. Compute \( 5g(-2) \) and \( 4h(-2) \).
  3. Subtract \( 4h(-2) \) from \( 5g(-2) \).
Step 1: Evaluate \( g(-2) \)

We start by substituting \( n = -2 \) into the function \( g(n) \): \[ g(-2) = -2(-2) - 2 = 4 - 2 = 2 \]

Step 2: Evaluate \( h(-2) \)

Next, we substitute \( n = -2 \) into the function \( h(n) \): \[ h(-2) = (-2)^2 + 5(-2) = 4 - 10 = -6 \]

Step 3: Compute \( 5g(-2) \) and \( 4h(-2) \)

Now we calculate \( 5g(-2) \) and \( 4h(-2) \): \[ 5g(-2) = 5 \times 2 = 10 \] \[ 4h(-2) = 4 \times (-6) = -24 \]

Step 4: Calculate \( (5g - 4h)(-2) \)

Finally, we find \( (5g - 4h)(-2) \): \[ (5g - 4h)(-2) = 10 - (-24) = 10 + 24 = 34 \]

Final Answer

The final result is \(\boxed{34}\).

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