Evaluate the expression:

[tex]\[ 3 \cdot f(-4) - 3 \cdot g(-2) = \square \][/tex]

Note: This question involves function notation. Please refer to your class materials or notes for definitions of the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex].



Answer :

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]