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Show that the function f: R->{x in R :-...

Show that the function `f: R->{x in R :-1ltxlt1}` defined by `f(x)=x/(1+|x|),x in R` is one-one and onto function.

Text Solution

Verified by Experts

`(i) f(x)=x/(1-x)`
Let `f(x_1)=f(x_2)`
`=>(x_1)/(1-x_1)=(x_2)/(1-x_2)`
`=>x_1-x_1x_2=x_2-x_1x_2`
...
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