https://file.aiquickdraw.com/mathbot/file/172803826190601sl5g6i.jpg

The problem in the image asks you to find \( (g - f)(-8) \) given that:

\[
f(x) = -8x + 2
\]
and
\[
g(x) = 4x
\]

### Step-by-Step Solution:

1. **Interpret the expression \( (g - f)(x) \)**:
   \[
   (g - f)(x) = g(x) - f(x)
   \]
   Using the given functions:
   \[
   (g - f)(x) = 4x - (-8x + 2)
   \]
   Simplify the expression:
   \[
   (g - f)(x) = 4x + 8x - 2 = 12x - 2
   \]

2. **Substitute \( x = -8 \) into the expression**:
   \[
   (g - f)(-8) = 12(-8) - 2
   \]
   Simplify:
   \[
   (g - f)(-8) = -96 - 2 = -98
   \]

Thus, the value of \( (g - f)(-8) \) is \(-98\).

Would you like any more details or explanations? Here are some related questions you can explore:

1. How do you find the difference of two functions in general?
2. How would this problem change if the expression was \( (f - g)(-8) \) instead of \( (g - f)(-8) \)?
3. What is the geometric interpretation of \( (g - f)(x) \)?
4. How would the solution change if \( g(x) \) was a more complex function, like \( g(x) = 4x^2 \)?
5. Can you generalize a method to evaluate expressions like \( (g - f)(a) \) for arbitrary \( a \)?

### Tip: 
Always simplify expressions before substituting specific values, as it makes the calculation much easier and reduces potential errors.

Find (g - f)(-8) if f(x) = -8x + 2 and g(x) = 4x

Solve the function subtraction problem: Find (g - f)(-8) where f(x) = -8x + 2 and g(x) = 4x. Learn step-by-step how to subtract functions and substitute values for x. Suitable for students in Grades 9-11.

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