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Show that the function f: R0->R0 , defin...

Show that the function `f: R_0->R_0` , defined as `f(x)=1/x` , is one-one onto, where `R_0` is the set of all non-zero real numbers. Is the result true, if the domain `R_0` is replaced by `N` with co-domain being same as `R_0` ?

Text Solution

Verified by Experts

Solving for `f:R->R`
putting `f(x_1)=f(x_2)`
`1/(x_1)=1/(x_2)`
`x_2=x_1`
...
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