I hope u meant f=1\T.
Otherwise question will not be valid.Below it is shown how we get f=1/T
Since,frequency is defined as the number of oscillations produced in 1 second.
i.e., f vibration is produced in 1 second
Therefore, 1 vibration is produced in 1/fsecond
But, by definition ;
Time taken to produce 1 oscillation is called time-period.
Obviously,
T=1/f (Where T=time-period & f=frequency)