Find the inverse of f(x)=x+3�(�)=�+3.

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

1. **Rewrite the function**: 
   \[
   y = x + 3
   \]

2. **Express \( x \) in terms of \( y \)**:
   \[
   y = x + 3
   \]
   Subtract 3 from both sides:
   \[
   y - 3 = x
   \]

3. **Swap \( x \) and \( y \)** to find the inverse function:
   \[
   x = y - 3
   \]

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

Would you like more details on this process or have any other questions?

Here are 8 related questions that expand on this topic:

1. What is the domain and range of the inverse function \( f^{-1}(x) = x - 3 \)?
2. How do you verify that \( f(x) \) and \( f^{-1}(x) \) are indeed inverses of each other?
3. How would the process of finding the inverse change if the function were \( f(x) = x - 3 \)?
4. What is the graphical interpretation of finding the inverse of a function?
5. How can you determine if a function is one-to-one and thus has an inverse?
6. What are the properties of a function and its inverse regarding their compositions?
7. How does the horizontal line test relate to finding the inverse of a function?
8. What are some practical applications of inverse functions in real life?

**Tip:** When finding an inverse function, always double-check by composing the original function and its inverse. The result should be the identity function: \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \).

Learn how to find the inverse of the function f(x) = x + 3 step-by-step. This problem covers functions and inverse functions, demonstrating the process of rewriting the function, solving for x in terms of y, and swapping variables to find the inverse. Suitable for students in Grades 10-12.

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