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.