The function given is \( f(x) = x \).

To find the inverse of a function \( f(x) \), we follow these steps:

1. Replace \( f(x) \) with \( y \):
   \[
   y = x
   \]

2. Swap \( x \) and \( y \) (this step reflects the function over the line \( y = x \)):
   \[
   x = y
   \]

3. Solve for \( y \):
   \[
   y = x
   \]

Thus, the inverse of \( f(x) = x \) is itself, meaning:
\[
f^{-1}(x) = x
\]

This makes sense because \( f(x) = x \) is a linear function with a slope of 1, and such functions are their own inverses.

Would you like any details or further clarifications on this?

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Here are 5 related questions you might explore:
1. What is the inverse of \( f(x) = 2x + 3 \)?
2. How do you verify if two functions are inverses of each other?
3. How would the graph of \( f(x) = x \) and its inverse look?
4. What is the inverse of a quadratic function like \( f(x) = x^2 \)?
5. What happens if a function doesn't have an inverse?

**Tip:** A function must be one-to-one (bijective) to have an inverse, meaning every output corresponds to exactly one input.

Learn how to find the inverse of the linear function f(x) = x with a detailed step-by-step explanation. Understand the concept of inverse functions and the special case where the function is its own inverse. Suitable for students in Grades 8-10.

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