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Show that the function f: R → R: f(x) = x4 is neither one-one nor onto.

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It is given that

f(x) = x4

By substituting the values

f(1) = 14 = 1

f(-1) = -14 = 1

Hence, f is many-one.

Consider -1 in the co-domain R with no x ∈ R such that f(x) = x4 = – 1

f is into.

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