Find the value of `f(f(-2))`, if `f(x)=(x)/(x+1)`

Options

A. `3//2`
B. `4//3`
C. `2//3`
D. None of these

Answer

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

### Step 1: Calculate \( f(-2) \)
We start by substituting \(-2\) into the function \( f(x) \).

\[ f(-2) = \frac{-2}{-2 + 1} \]

Calculating the denominator:

\[ -2 + 1 = -1 \]

Now substituting back into the function:

\[ f(-2) = \frac{-2}{-1} = 2 \]

### Step 2: Calculate \( f(f(-2)) \)
Now that we have \( f(-2) = 2 \), we need to find \( f(2) \).

\[ f(2) = \frac{2}{2 + 1} \]

Calculating the denominator:

\[ 2 + 1 = 3 \]

Now substituting back into the function:

\[ f(2) = \frac{2}{3} \]

### Final Answer
Thus, the value of \( f(f(-2)) \) is

\[ \frac{2}{3} \]

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