If `f (x) =x ^(2) -6x + 9, 0 le x le 4, ` then `f(3) =`

Options

A. 4
B. 1
C. 0
D. does not exist

Answer

To find the value of \( f(3) \) for the function \( f(x) = x^2 - 6x + 9 \) where \( 0 \leq x \leq 4 \), we can follow these steps:

### Step 1: Identify the function and the value to substitute
We have the function:
\[ f(x) = x^2 - 6x + 9 \]
We need to find \( f(3) \).

### Step 2: Substitute \( x = 3 \) into the function
Now, we will substitute \( x \) with \( 3 \):
\[ f(3) = 3^2 - 6 \cdot 3 + 9 \]

### Step 3: Calculate \( 3^2 \)
Calculating \( 3^2 \):
\[ 3^2 = 9 \]

### Step 4: Calculate \( -6 \cdot 3 \)
Now, calculate \( -6 \cdot 3 \):
\[ -6 \cdot 3 = -18 \]

### Step 5: Combine the results
Now we can combine all parts:
\[ f(3) = 9 - 18 + 9 \]

### Step 6: Simplify the expression
Now simplify:
\[ f(3) = 9 - 18 + 9 = 0 \]

### Final Answer
Thus, \( f(3) = 0 \).

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