Question

show that the function $f : R \dashrightarrow R$ defined by f ( x ) = $\frac{1}{x}$ is one - one but not onto.

thankyou! :)​

Answer 1

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

The given function is :

$\qquad \tt \dashrightarrow \:f(x) = \frac{1}{x}$

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 ]