To solve the given expression, we need to evaluate the functions \( f(x) \) and \( g(x) \) at specific points and then perform the necessary arithmetic operations. Here’s a detailed, step-by-step solution:
1. Evaluate \( f(-4) \):
We are given the function \( f(x) \) and need to evaluate it at \( x = -4 \). The value of \( f(-4) \) is:
[tex]\[
f(-4) = -7
\][/tex]
2. Evaluate \( g(-2) \):
Similarly, we need to evaluate the function \( g(x) \) at \( x = -2 \). The value of \( g(-2) \) is:
[tex]\[
g(-2) = 5
\][/tex]
3. Substitute these values into the expression \( 3 \cdot f(-4) - 3 \cdot g(-2) \):
[tex]\[
3 \cdot f(-4) = 3 \cdot (-7) = -21
\][/tex]
[tex]\[
3 \cdot g(-2) = 3 \cdot 5 = 15
\][/tex]
4. Combine the results from the previous step:
[tex]\[
3 \cdot f(-4) - 3 \cdot g(-2) = -21 - 15 = -36
\][/tex]
So, the final result is:
[tex]\[
3 \cdot f(-4) - 3 \cdot g(-2) = -36
\][/tex]
