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We are tasked with finding and simplifying the expression \((f - g)(1)\), where:

\[
f(x) = \sqrt{x + 3} \quad \text{and} \quad g(x) = x^2 - x.
\]

To calculate \((f - g)(1)\), we will follow these steps:

### Step 1: Find \(f(1)\)
\[
f(1) = \sqrt{1 + 3} = \sqrt{4} = 2.
\]

### Step 2: Find \(g(1)\)
\[
g(1) = 1^2 - 1 = 1 - 1 = 0.
\]

### Step 3: Calculate \((f - g)(1)\)
\[
(f - g)(1) = f(1) - g(1) = 2 - 0 = 2.
\]

Thus, \((f - g)(1) = 2\).

Would you like further details on the steps, or do you have any questions?

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Here are 5 related questions:
1. How would you calculate \((f + g)(1)\) with the same functions?
2. What is the general formula for \((f - g)(x)\) for any \(x\)?
3. How do you solve \((f - g)(x) = 0\)?
4. Can you find the derivative of \(f(x)\) and \(g(x)\)?
5. What happens to \(f(x)\) and \(g(x)\) as \(x\) approaches infinity?

**Tip:** Always substitute the values carefully, especially under the square root, to avoid errors.

Let f(x) = √(x + 3) and g(x) = x² - x. Find and simplify the expression (f - g)(1).

Learn how to simplify the expression (f - g)(1) where f(x) = √(x + 3) and g(x) = x² - x. This problem covers essential algebraic concepts like function evaluation, square roots, and combining functions. Suitable for students in Grades 9-10.

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