Given f(x) = x - 5 and g(x) = x²-1 h(x) = 2x + 1. Find the following:

1. a. (f+g)x

To find \((f+g)(x)\), we need to add the two functions \( f(x) \) and \( g(x) \):

Given:
- \( f(x) = x - 5 \)
- \( g(x) = x^2 - 1 \)

\[
(f + g)(x) = f(x) + g(x)
\]
\[
(f + g)(x) = (x - 5) + (x^2 - 1)
\]

Now, simplify:
\[
(f + g)(x) = x^2 + x - 5 - 1
\]
\[
(f + g)(x) = x^2 + x - 6
\]

So, \((f + g)(x) = x^2 + x - 6\).

Would you like more details or explanations on any steps?

Here are some related questions you might consider:

1. b. \((f - g)(x)\)
2. c. \((f \cdot g)(x)\)
3. d. \((g \cdot h)(x)\)
4. e. Find \( f(g(x)) \)
5. f. Find \( h(f(x)) \)

**Tip:** Always start by breaking down each function into its components before performing operations like addition, subtraction, or composition!

Given f(x) = x - 5 and g(x) = x² - 1, h(x) = 2x + 1. Find the following: 1. a. (f+g)x

Learn how to find (f+g)(x) by adding functions f(x) = x - 5 and g(x) = x² - 1. This problem involves key algebraic concepts, such as function operations and simplifying polynomials. Suitable for students in Grades 9-10.

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