The range of the function `f(x)=(x-2)/(2-x)` is

Options

A. R
B. R - {1}
C. {-1}
D. R - { - l}

Answer

To find the range of the function \( f(x) = \frac{x-2}{2-x} \), we can follow these steps:

### Step 1: Rewrite the function
First, we can rewrite the function to simplify it. Notice that we can factor out a negative sign from the denominator:

\[ f(x) = \frac{x-2}{2-x} = \frac{x-2}{-(x-2)} = -1 \quad \text{(for } x \neq 2\text{)} \]

### Step 2: Identify the nature of the function
From the simplification, we see that \( f(x) = -1 \) for all values of \( x \) except \( x = 2 \). This indicates that the function is constant.

### Step 3: Determine the range
Since \( f(x) \) is constant and equals \(-1\) for all \( x \) in its domain (except at \( x = 2 \)), the range of the function is simply:

\[ \text{Range} = \{-1\} \]

### Final Answer
Thus, the range of the function \( f(x) = \frac{x-2}{2-x} \) is:

\[ \text{Range} = \{-1\} \]

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