If
f(x)=x
2
−2,
g(x)=3x−4, and
h(x)=2−4x , find
(f−g)(x).

To find \((f - g)(x)\), you need to subtract the function \(g(x)\) from \(f(x)\):

Given:
- \( f(x) = x^2 - 2 \)
- \( g(x) = 3x - 4 \)

Now, \((f - g)(x)\) is defined as:

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

Substitute the expressions for \(f(x)\) and \(g(x)\):

\[
(f - g)(x) = (x^2 - 2) - (3x - 4)
\]

Distribute the negative sign:

\[
(f - g)(x) = x^2 - 2 - 3x + 4
\]

Simplify the expression:

\[
(f - g)(x) = x^2 - 3x + 2
\]

So, the result is:

\[
(f - g)(x) = x^2 - 3x + 2
\]

Let me know if you'd like more details or have any questions! Here are five related questions:

1. How do you find the difference of two functions in general?
2. What is the domain of the resulting function \((f - g)(x)\)?
3. How would you find the zeros of \((f - g)(x)\)?
4. How does subtracting functions relate to adding functions?
5. How do function transformations affect the graph of \((f - g)(x)\)?

**Tip**: Always simplify the resulting expression when combining functions, especially when subtracting or adding!

If f(x)=x^2−2, g(x)=3x−4, and h(x)=2−4x , find (f−g)(x).

Learn how to find the difference between two functions, f(x) = x^2 − 2 and g(x) = 3x − 4. This step-by-step solution simplifies the expression to (f − g)(x) = x^2 − 3x + 2, covering key algebraic concepts and function operations. Suitable for students in Grades 8-10.

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