Let's work through the problems based on the functions given in the image:

We have two functions:

• $f(x) = 1 - 11x$
• $g(x) = x^2 - x + 15$

(a) Find $g(-2)$:

Substitute $x = -2$ into $g(x)$: $g(-2) = (-2)^2 - (-2) + 15 = 4 + 2 + 15 = 21$ Thus, $g(-2) = 21$.

(b) Find $f(7) - g(-2)$:

We already know from part (a) that $g(-2) = 21$.

Now, calculate $f(7)$: $f(7) = 1 - 11(7) = 1 - 77 = -76$

Now, subtract $g(-2)$ from $f(7)$: $f(7) - g(-2) = -76 - 21 = -97$ Thus, $f(7) - g(-2) = -97$.

(c) Find $g(3) \cdot f(2)$:

First, calculate $g(3)$: $g(3) = (3)^2 - 3 + 15 = 9 - 3 + 15 = 21$

Now, calculate $f(2)$: $f(2) = 1 - 11(2) = 1 - 22 = -21$

Finally, multiply $g(3)$ and $f(2)$: $g(3) \cdot f(2) = 21 \cdot (-21) = -441$ Thus, $g(3) \cdot f(2) = -441$.

If you have any questions or want further details on the steps, feel free to ask! Here are five additional related questions:

1. What is the value of $f(-5)$?
2. What happens to $g(x)$ when $x = 0$?
3. What is the result of $f(10) + g(10)$?
4. Can you solve $f(x) = g(x)$ for $x$?
5. What is the product $f(-3) \cdot g(2)$?

Tip: Always check your substitutions carefully to avoid simple mistakes, especially when working with negative signs.