If f(x) = 3x – 4, then what is f^-1(x)?

To find the inverse of the function \( f(x) = 3x - 4 \), follow these steps:

1. **Replace \( f(x) \) with \( y \):**
   \[
   y = 3x - 4
   \]
2. **Swap \( x \) and \( y \) to solve for \( y \):**
   \[
   x = 3y - 4
   \]
3. **Solve for \( y \):**
   \[
   x + 4 = 3y
   \]
   \[
   y = \frac{x + 4}{3}
   \]

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

Would you like more details or have any questions?

Here are 5 related questions to practice:

1. If \( f(x) = 2x + 5 \), what is \( f^{-1}(x) \)?
2. For \( f(x) = \frac{1}{2}x - 7 \), find the inverse function.
3. If \( f(x) = x^2 + 3 \), can you find the inverse? Why or why not?
4. Find the inverse of \( f(x) = 5x^2 \) for \( x \geq 0 \).
5. Given \( f^{-1}(x) = \frac{x}{3} - 1 \), what is \( f(x) \)?

**Tip:** To check if a function is the correct inverse, compose \( f(f^{-1}(x)) \) and \( f^{-1}(f(x)) \); both should return \( x \).

Discover how to find the inverse of the function f(x) = 3x - 4 in this detailed step-by-step solution. Learn about inverse functions and key algebraic concepts involved, suitable for students in Grades 9-10.

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