Find the inverse function of the function f, of, x, equals, 5, x, plus, 7f(x)=5x+7.

To find the inverse of the function \( f(x) = 5x + 7 \), follow these steps:

1. **Replace \( f(x) \) with \( y \):**
   \[
   y = 5x + 7
   \]

2. **Swap \( x \) and \( y \):**  
   The inverse function is found by interchanging \( x \) and \( y \).
   \[
   x = 5y + 7
   \]

3. **Solve for \( y \):**  
   Isolate \( y \) to express it in terms of \( x \).
   \[
   x - 7 = 5y
   \]
   \[
   y = \frac{x - 7}{5}
   \]

4. **Replace \( y \) with \( f^{-1}(x) \):**
   The inverse function is:
   \[
   f^{-1}(x) = \frac{x - 7}{5}
   \]

Thus, the inverse of the function \( f(x) = 5x + 7 \) is:
\[
f^{-1}(x) = \frac{x - 7}{5}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What is the graphical interpretation of a function and its inverse?
2. How do you verify if two functions are inverses of each other?
3. How does the domain and range of a function change when finding its inverse?
4. What are some common mistakes to avoid when solving for the inverse of a function?
5. Can all linear functions have inverses?

**Tip:** To check if you found the correct inverse, apply both functions and ensure \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \).

Find the inverse function of the function f(x) = 5x + 7.

Learn how to find the inverse function of f(x) = 5x + 7 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inverse functions and properties of linear functions. Suitable for students in Grades 9-11.

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