Let `A={-2,\ -1,\ 0,\ 1,\ 2}a n d\ f: A->ZZ` be given y `f(x)=x^2-2x-3.` Find: i. the range of `f` ii. pre images of `6,-3` and `5.`

Explanation

To solve the problem step by step, we will first find the range of the function \( f \) defined as \( f(x) = x^2 - 2x - 3 \) for the set \( A = \{-2, -1, 0, 1, 2\} \). Then, we will find the pre-images of the values \( 6, -3, \) and \( 5 \).

### Step 1: Calculate \( f(x) \) for each element in \( A \)

1. **For \( x = -2 \)**:
\[ f(-2) = (-2)^2 - 2(-2) - 3 = 4 + 4 - 3 = 5 \]
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