If f(x) is a linear function and the slope of `y=f(x)` is `(1)/(2)`, what is the slope of `y = f^(-1)(x)` ?

Options

A. `-2`
B. `-(1)/(2)`
C. `(1)/(2)`
D. 2

Explanation

To find the slope of the inverse function \( y = f^{-1}(x) \) given that the slope of \( y = f(x) \) is \( \frac{1}{2} \), we can use the relationship between the slopes of a function and its inverse.

### Step-by-Step Solution:

1. **Understand the relationship between the slopes**:
The slope of the function \( f(x) \) is denoted as \( m \). For the inverse function \( f^{-1}(x) \), the slope \( m' \) is given by the formula:
\[ m' = \frac{1}{m} \]
where \( m \) is the slope of \( f(x) \).

2. **Identify the given slope**:
From the problem, we know that the slope of \( f(x) \) is:
\[ m = \frac{1}{2} \]

3. **Calculate the slope of the inverse function**:
Using the formula for the slope of the inverse function:
\[ m' = \frac{1}{m} = \frac{1}{\frac{1}{2}} = 2 \]

4. **Conclusion**:
Therefore, the slope of \( y = f^{-1}(x) \) is:
\[ m' = 2 \]

### Final Answer:
The slope of \( y = f^{-1}(x) \) is \( 2 \).