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Question
How many of the following are functions ?
(i) f(x) = x5;{−1,0,1}→{0,1,2}
(ii) f(x) = ∓√x;{0,4,9}→{0,2,−2,3,−3}
(iii) f(x) = √x;{0,4,9}→{0,2,−2,3,−3}
(iv) f(x) = x2;{0,1,2}→{0,1,2,3,4}
How many of the following are functions ?
(i) f(x) = x5;{−1,0,1}→{0,1,2}
(ii) f(x) = ∓√x;{0,4,9}→{0,2,−2,3,−3}
(iii) f(x) = √x;{0,4,9}→{0,2,−2,3,−3}
(iv) f(x) = x2;{0,1,2}→{0,1,2,3,4}
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Solution
The correct option is D (iii) & (iv)
(i) f (-1) = -1, but there is no -1 in the second set. So its not a function
(ii) f(4) = ± 2, in a function, an element will be mapped to only one element. So, (ii) is not a function as 4 is mapped to both 2 and -2.
(iii) and (iv) are functions as they satisfy the definition of function.(i.e, each element in the first set has one and only one image)
(iii) & (iv)
(i) f (-1) = -1, but there is no -1 in the second set. So its not a function
(ii) f(4) = ± 2, in a function, an element will be mapped to only one element. So, (ii) is not a function as 4 is mapped to both 2 and -2.
(iii) and (iv) are functions as they satisfy the definition of function.(i.e, each element in the first set has one and only one image)
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