determine (f+g)(4) when f(x) =x^2-3 and g(x)=6/x-2

To determine \((f+g)(4)\), we need to add the values of \(f(4)\) and \(g(4)\).

We are given the functions:

- \(f(x) = x^2 - 3\)
- \(g(x) = \frac{6}{x} - 2\)

### Step 1: Calculate \(f(4)\)

\[
f(4) = 4^2 - 3 = 16 - 3 = 13
\]

### Step 2: Calculate \(g(4)\)

\[
g(4) = \frac{6}{4} - 2 = 1.5 - 2 = -0.5
\]

### Step 3: Add \(f(4)\) and \(g(4)\)

\[
(f + g)(4) = f(4) + g(4) = 13 + (-0.5) = 12.5
\]

### Final Answer:
\[
(f + g)(4) = 12.5
\]

Would you like further clarification or more details on the steps?

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Here are 5 questions to expand your understanding:

1. What is the difference between \((f+g)(x)\) and \((f \cdot g)(x)\)?
2. How would you calculate \((f-g)(4)\) for the given functions?
3. Can you graph \(f(x)\) and \(g(x)\) and analyze where they intersect?
4. What happens if \(g(x)\) has a denominator of zero? How does that affect the function's domain?
5. How would you compute the composition of \(f\) and \(g\), i.e., \(f(g(x))\)?

**Tip:** When dealing with rational functions like \(g(x)\), always check for values that make the denominator zero, as these are excluded from the domain.

Learn how to solve (f+g)(4) by adding the functions f(x) = x^2 - 3 and g(x) = 6/x - 2. This problem covers key algebraic concepts, including function addition and rational functions. Suitable for students in Grades 8-10.

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