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If f={(1,2,),(2,-3),(3,-1)}, then find t...

If `f={(1,2,),(2,-3),(3,-1)}`, then find the domain and range of f.

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To find the domain and range of the function \( f = \{(1, 2), (2, -3), (3, -1)\} \), we will follow these steps: ### Step 1: Identify the Ordered Pairs The function \( f \) is given as a set of ordered pairs: - \( (1, 2) \) - \( (2, -3) \) - \( (3, -1) \) ### Step 2: Determine the Domain The domain of a function consists of all the first elements (or inputs) of the ordered pairs. From the ordered pairs: - The first element of \( (1, 2) \) is \( 1 \) - The first element of \( (2, -3) \) is \( 2 \) - The first element of \( (3, -1) \) is \( 3 \) Thus, the domain of \( f \) is: \[ \text{Domain of } f = \{1, 2, 3\} \] ### Step 3: Determine the Range The range of a function consists of all the second elements (or outputs) of the ordered pairs. From the ordered pairs: - The second element of \( (1, 2) \) is \( 2 \) - The second element of \( (2, -3) \) is \( -3 \) - The second element of \( (3, -1) \) is \( -1 \) Thus, the range of \( f \) is: \[ \text{Range of } f = \{2, -3, -1\} \] ### Final Answer - **Domain of \( f \)**: \( \{1, 2, 3\} \) - **Range of \( f \)**: \( \{2, -3, -1\} \) ---
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