Find the inverse functions of the following one-to-one functions:
Example:

Step l = y = x + 3

Step 2. x = y + 3

Step 3 = x - 3 = y or y = x - 3

Step 4 = f - 1(x) = x - 3

Step 1. Replace f(x) by y)

Step 2. (Interchange x's and y's)

Step 3. (Solve for y in step 2)

Step 4. (Replace y with f-1)

Solve this 3: 
1. f(x) = (x + 3)^3
2. f(x) = 1/2 x + 4
3. f(x) = 4

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.

Find the inverse functions of the following one-to-one functions:
1. f(x) = (x + 3)^3
2. f(x) = 1/2 x + 4
3. f(x) = 4

Learn how to find the inverse of one-to-one functions with step-by-step solutions for f(x) = (x + 3)^3, f(x) = 1/2x + 4, and understand why constant functions like f(x) = 4 do not have an inverse. Suitable for Grades 10-12.

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