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We are given a linear function \( f(x) \), and it is stated that:

- \( f(2) = 10 \)
- We are asked to find \( f^{-1}(10) \), where \( f^{-1}(x) \) is the inverse of the function \( f(x) \).

### Step-by-step solution:

1. **Linear Function Property**:  
   Since \( f(x) \) is linear, we can express it in the form:
   \[
   f(x) = ax + b
   \]
   where \( a \) and \( b \) are constants.

2. **Using the Information \( f(2) = 10 \)**:
   Substituting \( x = 2 \) into the equation \( f(x) = ax + b \):
   \[
   f(2) = a(2) + b = 10
   \]
   This simplifies to:
   \[
   2a + b = 10 \quad \text{(Equation 1)}
   \]

3. **What is \( f^{-1}(10) \)?**
   The inverse function \( f^{-1}(x) \) reverses the roles of \( x \) and \( f(x) \), so we need to find \( x \) such that \( f(x) = 10 \).

   But from the problem, we are already given that \( f(2) = 10 \). This means the input \( x = 2 \) gives the output \( f(x) = 10 \).

   Therefore, \( f^{-1}(10) = 2 \), because the inverse function maps 10 back to 2.

### Conclusion:
The value of \( f^{-1}(10) \) is 2, so the correct answer is:

**b. 2**

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Would you like a detailed explanation on any of these steps? Here are 5 related questions you might find interesting:

1. What is the general method for finding the inverse of a linear function?
2. How would you solve for the constants \( a \) and \( b \) if given two points on a linear function?
3. Why is the inverse of a linear function also a function?
4. How do you graphically interpret the relationship between a function and its inverse?
5. What conditions must be satisfied for a function to have an inverse?

**Tip**: For a function to have an inverse, it must be one-to-one, meaning that each output is associated with exactly one input.

The function f(x) is a linear function, and f(2) = 10. What is the value of f^(-1)(10)?

Solve a problem involving linear functions and their inverses, where f(2)=10. Learn how to calculate f^(-1)(10) by using properties of linear equations. This is suitable for students in Grades 8-10.

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