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.