Consider the function f(x)=`(x-1)/(x+1)`
What is f(2x) equal to?

Options

A. `(f(x)+1)/(f(x)+3)`
B. `(f(x)+1)/(3f(x)+1)`
C. `(3f(x)+1)/(f(x)+3)`
D. `(f(x)+3)/(3f(x)+1)`

Answer

To find \( f(2x) \) for the function \( f(x) = \frac{x-1}{x+1} \), we will follow these steps:

### Step 1: Substitute \( 2x \) into the function
We start by substituting \( 2x \) into the function \( f(x) \):
\[ f(2x) = \frac{2x - 1}{2x + 1} \]

### Step 2: Simplify the expression
The expression \( f(2x) = \frac{2x - 1}{2x + 1} \) is already in its simplest form, so we will keep it as is.

### Step 3: Analyze the function
We can observe that the function \( f(x) \) has a specific structure. The numerator is \( 2x - 1 \) and the denominator is \( 2x + 1 \).

### Step 4: Verify if further simplification is possible
Since \( f(2x) \) is already simplified, we can express it in terms of \( f(x) \):
\[ f(2x) = \frac{2(x - \frac{1}{2})}{2(x + \frac{1}{2})} = \frac{x - \frac{1}{2}}{x + \frac{1}{2}} \cdot 2 \]
However, this does not lead to a simpler form than \( \frac{2x - 1}{2x + 1} \).

### Final Result
Thus, the final expression for \( f(2x) \) is:
\[ f(2x) = \frac{2x - 1}{2x + 1} \]