What is the value of f(-2) if f(x) =`(x^2+4x-8)/(x-2)`?

Options

A. -3
B. -1
C. 1
D. 3

Answer

To find the value of \( f(-2) \) for the function \( f(x) = \frac{x^2 + 4x - 8}{x - 2} \), we will follow these steps:

### Step 1: Substitute -2 into the function
We need to substitute \( x = -2 \) into the function \( f(x) \).

\[ f(-2) = \frac{(-2)^2 + 4(-2) - 8}{-2 - 2} \]

### Step 2: Calculate the numerator
Now, let's calculate the numerator:

\[ (-2)^2 = 4 \]
\[ 4(-2) = -8 \]
So, the numerator becomes:

\[ 4 - 8 - 8 = 4 - 16 = -12 \]

### Step 3: Calculate the denominator
Now, calculate the denominator:

\[ -2 - 2 = -4 \]

### Step 4: Combine the results
Now, we can combine the results from the numerator and denominator:

\[ f(-2) = \frac{-12}{-4} \]

### Step 5: Simplify the fraction
Now, simplify the fraction:

\[ f(-2) = 3 \]

Thus, the value of \( f(-2) \) is \( 3 \).

### Final Answer:
\[ f(-2) = 3 \]

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