Compute f(f−1(x))**.**Find the equation for the inverse f−1(x).

To solve the problem, we will first find the inverse of the function \( f(x) \), then compute \( f(f^{-1}(x)) \).

### Step 1: Find the equation for the inverse \( f^{-1}(x) \)

To find the inverse, follow these steps:

1. Start with \( y = f(x) \). 
2. Swap \( x \) and \( y \): \( x = f(y) \).
3. Solve for \( y \), which gives \( f^{-1}(x) \).

The function you are working with is not provided, so I'll explain the general approach. If you have a specific function \( f(x) \) in mind, please provide it, and I'll apply the steps to that particular function.

### Step 2: Compute \( f(f^{-1}(x)) \)

For any function \( f \) and its inverse \( f^{-1} \), the identity \( f(f^{-1}(x)) = x \) holds true. This means that when you compose a function with its inverse, the result is always the original input \( x \).

Thus, \( f(f^{-1}(x)) = x \).

#### Summary:

1. **Inverse of \( f(x) \)**: To find the inverse, swap \( x \) and \( y \) in \( f(x) = y \), then solve for \( y \).
2. **Composition of a function with its inverse**: \( f(f^{-1}(x)) = x \).

Let me know if you have a specific function for which you need to find the inverse, or if you'd like a more detailed breakdown.

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Would you like a step-by-step solution for a particular function? Here are some examples of related questions:

1. How do I find the inverse of \( f(x) = 3x + 2 \)?
2. How do I solve for \( f^{-1}(x) \) when \( f(x) = \frac{x-1}{x+2} \)?
3. Can you explain the graphical interpretation of \( f(f^{-1}(x)) = x \)?
4. What is the inverse of an exponential function like \( f(x) = e^x \)?
5. How does the inverse function work for quadratic functions?

**Tip**: The inverse of a function essentially "reverses" the effect of the original function. To ensure an inverse exists, the original function must be one-to-one (bijective).

Compute f(f−1(x)). Find the equation for the inverse f−1(x).

This guide explains how to compute f(f−1(x)) and find the inverse of a function, with step-by-step instructions and key mathematical concepts such as the inverse function theorem. Suitable for high school students in Grades 10-12.

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