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### Problem 1:
You are asked to find the inverse of the function \( f(x) = 3x - 4 \).

**Steps to find the inverse:**

1. Start with \( f(x) = y = 3x - 4 \).
2. Solve for \( x \) in terms of \( y \):
   \[
   y = 3x - 4 \implies x = \frac{y + 4}{3}
   \]
3. Replace \( y \) with \( x \) to express the inverse:
   \[
   f^{-1}(x) = \frac{x + 4}{3}
   \]

Thus, the inverse of the function is \( f^{-1}(x) = \frac{x + 4}{3} \).

### Problem 2:
You are given \( f(x) = 2x + 3 \), and you're asked to find \( f^{-1}(x) \).

**Steps to find the inverse:**

1. Start with \( f(x) = y = 2x + 3 \).
2. Solve for \( x \) in terms of \( y \):
   \[
   y = 2x + 3 \implies x = \frac{y - 3}{2}
   \]
3. Replace \( y \) with \( x \):
   \[
   f^{-1}(x) = \frac{x - 3}{2}
   \]

Thus, the inverse of the function is \( f^{-1}(x) = \frac{x - 3}{2} \), which corresponds to the third option in Question 2.

Would you like further clarification or details on these steps?

### Follow-up Questions:
1. How would you find the inverse of a quadratic function?
2. What does it mean for a function to be "one-to-one"?
3. Can all functions have an inverse? Why or why not?
4. How do you graphically interpret the inverse of a function?
5. What are the conditions under which a function's inverse is also a function?

**Tip:** Always check that the inverse function, when composed with the original function, returns the identity \( f(f^{-1}(x)) = x \).

Find the inverse of the one-to-one function f(x) = 3x - 4. If f(x) = 2x + 3, then f^-1(x) = ________.

Learn how to find the inverse of the linear functions f(x) = 3x - 4 and f(x) = 2x + 3 with detailed step-by-step solutions. Understand key algebraic concepts such as inverse functions and the use of the inverse function theorem. Suitable for students in Grades 7-9.

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