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Prove that the function f: R → R: f(x) = 2x is one-one and onto.

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We know that

f (x1) = f (x2)

So we get

2x1 = 2x2 => x1 = x2

Here, f is one-one

Consider y = 2x where x = ½ y

Each y in co domain R there exists ½ y where

f (1/2 y) = (2 × ½ y) = y

Hence, f is onto.

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