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Check the injective and surjective of th...

Check the injective and surjective of the following functions : `f : Z rarr Z` given by `f(x) = x^2`

Text Solution

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We have `f(-1) = (-1)^2 = 1` and
`f(1) = 1^2 =1 `
`therefore` f maps both -1 and 1 to 1
`therefore ` f is not injective
Since square of an integers can.t exist an integer x satisfying `x^3 = -1 `
`therefore,` f is not a subjective
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