Given 
f(x)=x 
2
 −1, 
g(x)=2x−3, and 
h(x)=1−4x, perform the function operation 
(f−g)(x).

To perform the function operation \((f - g)(x)\), we subtract the function \(g(x)\) from the function \(f(x)\).

Given:
- \( f(x) = x^2 - 1 \)
- \( g(x) = 2x - 3 \)

### Step-by-step process:
\[
(f - g)(x) = f(x) - g(x)
\]

Substitute the expressions for \(f(x)\) and \(g(x)\):
\[
(f - g)(x) = (x^2 - 1) - (2x - 3)
\]

Distribute the negative sign:
\[
(f - g)(x) = x^2 - 1 - 2x + 3
\]

Now combine like terms:
\[
(f - g)(x) = x^2 - 2x + 2
\]

So, the result of \((f - g)(x)\) is:
\[
(f - g)(x) = x^2 - 2x + 2
\]

### Do you want any further details or have any questions?

Here are 5 related questions you could explore:
1. What is \((f + g)(x)\) using the same functions \(f(x)\) and \(g(x)\)?
2. How would you find \((f \cdot g)(x)\), the product of the functions?
3. Can you determine the domain of \((f - g)(x)\)?
4. What is \((g - h)(x)\) using \(g(x)\) and \(h(x)\)?
5. How would you solve for \(x\) if \((f - g)(x) = 0\)?

**Tip:** Always simplify expressions by distributing negative signs and combining like terms carefully to avoid mistakes!

Given f(x) = x^2 − 1, g(x) = 2x − 3, and h(x) = 1 − 4x, perform the function operation (f − g)(x).

Learn how to perform the function operation (f − g)(x) using the functions f(x) = x^2 − 1 and g(x) = 2x − 3. This problem demonstrates algebraic techniques for function subtraction and polynomial simplification. Suitable for students in Grades 9-10.

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