If `f(x) = x^(2) - 5x + 7` , then `f(2) - f(-1)` is equal to .

Options

A. `-34`
B. `34`
C. `12`
D. `-12`

Answer

To solve the problem, we need to calculate \( f(2) - f(-1) \) for the function \( f(x) = x^2 - 5x + 7 \).

### Step 1: Calculate \( f(2) \)
We start by substituting \( x = 2 \) into the function:
\[ f(2) = 2^2 - 5 \cdot 2 + 7 \]
Calculating each term:
\[ = 4 - 10 + 7 \]
Now, simplify:
\[ = 4 - 10 + 7 = 1 \]

### Step 2: Calculate \( f(-1) \)
Next, we substitute \( x = -1 \) into the function:
\[ f(-1) = (-1)^2 - 5 \cdot (-1) + 7 \]
Calculating each term:
\[ = 1 + 5 + 7 \]
Now, simplify:
\[ = 1 + 5 + 7 = 13 \]

### Step 3: Calculate \( f(2) - f(-1) \)
Now we can find \( f(2) - f(-1) \):
\[ f(2) - f(-1) = 1 - 13 \]
Simplifying this gives:
\[ = 1 - 13 = -12 \]

Thus, the final answer is:
\[ \boxed{-12} \]