https://file.aiquickdraw.com/mathbot/file/17280379229442f5ks09s.jpg

The problem shown in the image asks to find \( (g - f)(-8) \), given the functions:

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

### Step 1: Understanding the operation
The expression \( (g - f)(x) \) means subtracting the function \( f(x) \) from \( g(x) \):
\[
(g - f)(x) = g(x) - f(x)
\]

### Step 2: Substitute the functions for \( f(x) \) and \( g(x) \):
\[
(g - f)(x) = 4x - (-8x + 2)
\]
Simplify the expression:
\[
(g - f)(x) = 4x + 8x - 2
\]
\[
(g - f)(x) = 12x - 2
\]

### Step 3: Evaluate \( (g - f)(-8) \):
Now, substitute \( x = -8 \) into the expression \( 12x - 2 \):
\[
(g - f)(-8) = 12(-8) - 2
\]
\[
(g - f)(-8) = -96 - 2 = -98
\]

Thus, the solution is:
\[
(g - f)(-8) = -98
\]

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How do you graph the functions \( f(x) = -8x + 2 \) and \( g(x) = 4x \)?
2. What would \( (f - g)(x) \) look like if you reverse the order of subtraction?
3. How does the domain of \( f(x) \) and \( g(x) \) affect the domain of \( (g - f)(x) \)?
4. How can you find the x-intercepts of \( f(x) \) and \( g(x) \)?
5. How would you solve for \( (g - f)(x) = 0 \)?

**Tip**: Always simplify the inner functions before applying an operation like subtraction or addition to avoid calculation errors.

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

Learn how to solve the function operation (g - f)(x) when f(x) = -8x + 2 and g(x) = 4x. This step-by-step solution covers key algebraic concepts and function manipulation, including substitution and simplification. Suitable for students in Grades 8-10.

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