Let's solve the given functions one by one to find their inverse functions.

1. $f(x) = (x + 3)^3$

Step 1: Replace $f(x)$ by $y$. $y = (x + 3)^3$

Step 2: Interchange $x$ and $y$. $x = (y + 3)^3$

Step 3: Solve for $y$. $x^{1/3} = y + 3$ $y = x^{1/3} - 3$

Step 4: Replace $y$ with $f^{-1}(x)$. $f^{-1}(x) = x^{1/3} - 3$

2. $f(x) = \frac{1}{2}x + 4$

Step 1: Replace $f(x)$ by $y$. $y = \frac{1}{2}x + 4$

Step 2: Interchange $x$ and $y$. $x = \frac{1}{2}y + 4$

Step 3: Solve for $y$. $x - 4 = \frac{1}{2}y$ $y = 2(x - 4)$

Step 4: Replace $y$ with $f^{-1}(x)$. $f^{-1}(x) = 2(x - 4)$

3. $f(x) = 4$

Step 1: Replace $f(x)$ by $y$. $y = 4$

Step 2: Interchange $x$ and $y$. $x = 4$

Step 3: Solve for $y$ (but here, there's no variable to solve for). Since $f(x) = 4$ is a constant function, it does not have an inverse because it's not one-to-one.

Step 4: In this case, there's no inverse because the function is constant and fails the horizontal line test.

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If you have any questions or need further details, feel free to ask!

Here are some related questions to practice:

1. Find the inverse of $f(x) = (x - 2)^2$.
2. Find the inverse of $f(x) = \frac{3}{4}x + 5$.
3. Can you find the inverse of $f(x) = 7x^3 - 1$?
4. How do you check if a function has an inverse?
5. Find the inverse of $f(x) = \log(x + 2)$.

Tip: To determine if a function has an inverse, use the horizontal line test — if no horizontal line crosses the graph more than once, the function is one-to-one and has an inverse.