# Let Ro be the set of all nonzero real numbers. Then, show that the function f: Ro → Ro: f(x) = 1/x is one-one and onto.

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Let Ro be the set of all nonzero real numbers. Then, show that the function f: Ro → Ro: f(x) = 1/x is one-one and onto.

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We know that

f(x1) = f(x2)

It can be written as

1/x1 = 1/x2

So we get

x1 = x2

Hence, f is one-one.

Take y = 1/x

It can be written as

x = 1/y

Each y in co domain Ro there exists 1/y in domain Ro where f(1/y) = 1/(1/y) = y

Hence, f is onto.