https://file.aiquickdraw.com/mathbot/file/1726678450469ylk8irat.jpg

https://file.aiquickdraw.com/mathbot/file/17266784504721xbbw3tz.jpg

I have displayed both images to analyze the mathematical content. From the first image, we can see the functions:

\[
f(x) = x^2 + 8x - 9 \quad \text{and} \quad g(x) = x^2 - 2x + 15
\]

The question asks for \( f(x) - g(x) \).

To solve this, we subtract the two functions:

\[
f(x) - g(x) = (x^2 + 8x - 9) - (x^2 - 2x + 15)
\]

Now, let's simplify the expression:

\[
= x^2 + 8x - 9 - x^2 + 2x - 15
\]
\[
= (x^2 - x^2) + (8x + 2x) + (-9 - 15)
\]
\[
= 10x - 24
\]

So, the simplified expression for \( f(x) - g(x) \) is:

\[
f(x) - g(x) = 10x - 24
\]

You can now enter this expression without spaces as `10x-24`.

Would you like further details or have any other questions?

Here are some related questions to explore:

1. How do we derive the difference of two functions?
2. What happens if \( f(x) \) and \( g(x) \) have different degrees?
3. How would you graph the functions \( f(x) \) and \( g(x) \)?
4. What is \( f(x) + g(x) \)?
5. How can we use this difference \( f(x) - g(x) \) to find specific values of \( x \)?

**Tip:** When subtracting functions, always distribute the negative sign to all terms inside the parentheses to avoid mistakes.

Given f(x) = x^2 + 8x - 9 and g(x) = x^2 - 2x + 15, what is f(x) - g(x)?

Solve the subtraction of two polynomial functions: f(x) = x^2 + 8x - 9 and g(x) = x^2 - 2x + 15. Learn how to simplify the expression and arrive at the correct answer. This example helps with algebra concepts and polynomial operations, suitable for Grades 9-10.

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