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प्रश्न
Check the injectivity and surjectivity of the following function.
f : Z → Z given by f(x) = x2
उत्तर
f : Z → Z given by f(x) = x2
f(2) = 22 = 4 and f(– 2) = (– 2)2 = 4
∴ f(2) = f(– 2) but 2 ≠ – 2
∴ f is not injective
2 ∈ Z but there is no x ∈ Z such that 2 = f(x) = x2
∴ f is not surjective
∴ f is neither injective nor surjective.
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