Given that f(x)=x^2-6 and g(x)=18-x, find (f-g)(-10)

To find \((f - g)(-10)\), we need to subtract \(g(x)\) from \(f(x)\) and then evaluate the result at \(x = -10\).

1. \(f(x) = x^2 - 6\)
2. \(g(x) = 18 - x\)

\[
(f - g)(x) = f(x) - g(x) = (x^2 - 6) - (18 - x)
\]
Simplify the expression:

\[
(f - g)(x) = x^2 - 6 - 18 + x = x^2 + x - 24
\]

Now, substitute \(x = -10\) into this expression:

\[
(f - g)(-10) = (-10)^2 + (-10) - 24 = 100 - 10 - 24 = 66
\]

Thus, \((f - g)(-10) = 66\).

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. What is the general form of \((f \cdot g)(x)\) for the given functions?
2. How would you find the roots of the function \((f - g)(x)\)?
3. What is \((f + g)(x)\) for these functions?
4. How would you find the inverse of \(g(x)\)?
5. What is the domain and range of the function \(f(x)\)?

**Tip:** When simplifying expressions, make sure to distribute negatives properly to avoid errors.

Learn how to find (f - g)(-10) by subtracting the functions f(x) = x^2 - 6 and g(x) = 18 - x, and evaluating the result at x = -10. This step-by-step solution is ideal for algebra students in Grades 9-10, covering function operations and simplifying expressions.

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