If a function `f (x)` is given as `f (x) =x ^(2) -3x +2 ` for all `x in R, ` then `f (-1)=`

Options

A. 6
B. 0
C. 2
D. 8

Answer

To find the value of the function \( f(x) = x^2 - 3x + 2 \) at \( x = -1 \), we will substitute \(-1\) into the function and simplify.

### Step-by-Step Solution:

1. **Write down the function**:
\[ f(x) = x^2 - 3x + 2 \]

2. **Substitute \( x = -1 \)**:
\[ f(-1) = (-1)^2 - 3(-1) + 2 \]

3. **Calculate \((-1)^2\)**:
\[ (-1)^2 = 1 \]
So, we have:
\[ f(-1) = 1 - 3(-1) + 2 \]

4. **Calculate \(-3(-1)\)**:
\[ -3(-1) = 3 \]
Now, substitute this back into the equation:
\[ f(-1) = 1 + 3 + 2 \]

5. **Add the values together**:
\[ 1 + 3 = 4 \]
Then,
\[ 4 + 2 = 6 \]

6. **Final result**:
\[ f(-1) = 6 \]

### Conclusion:
The value of \( f(-1) \) is \( 6 \).

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