Show that the function f : R \dashrightarrow R defined by f ( x ) = (1)/(x) \\ is one - one but not onto. thankyou! :)​

Question

Show that the function
`f : R \dashrightarrow R` defined by f ( x ) =
`(1)/(x) \\` is one - one but not onto.

thankyou! :)​

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}`

The given function is :

`\qquad \tt \dashrightarrow \:f(x) = (1)/(x)`

here, for each value of x there is an unique value of f(x), so we can infer that it's a " one - one " function.

but it isn't an onto function because for value of x as 0, we have no value of f(x) [ undefined ]