https://file.aiquickdraw.com/mathbot/file/1728513613748quopvy2w.jpg

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, \( g(3) \cdot f(2) = -441 \).

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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.

Using the functions defined below, determine the indicated values: f(x) = 1 - 11x; g(x) = x^2 - x + 15

Learn how to solve functions such as f(x) = 1 - 11x and g(x) = x^2 - x + 15. This problem covers basic algebraic concepts, including function evaluation and arithmetic operations. Suitable for students in Grades 9-10.

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