Check whether , , (where [.] & {.} represent greatest integral and fractional part function respectively) is invertible or not, if yes, then (i)find its inverse. (ii)solve the equation .
Spoiler:
I was unable to do it. Any ideas?
Check whether , , (where [.] & {.} represent greatest integral and fractional part function respectively) is invertible or not, if yes, then (i)find its inverse. (ii)solve the equation .
Spoiler:
I was unable to do it. Any ideas?
Let .
,when is not an integer
Incase is an integer then which is obviously invertible.
Thus is clearly invertible.
Let be the inverse of
Since is not identically equal to .Therefore,solving is same as solving for .
On squaring,
is impossible
i.e. is an integer
According to...
Nearest Integer Function -- from Wolfram MathWorld
the notation indicates the 'nearest integer function' , so that ...
,
The function defined as...
,
is the so called 'floor function' and it is indicated as
Kind regards