I need to find the number of discontinuous point for
$$f(x)=[5x]+\{3x\}$$
where [] and {} are the G.I.F and the fractional part functions in the interval [0,5]
My attempt:
I wrote this as $[5x]-[3x]+3x$. Now the $[.]$ function is discontinuous at integer points. So, the points of discontinuity are -
$0,1/5,2/5,...,25/5$ for the $[5x]$ and
$0,1/3,2/3,...,15/3$ for the $[3x]$.
By inspection, $0,1,2,3,4,5$ belong to both $[5x]$ & $[3x]$ and they are not discontinuous.
But I am still taking some extra points as answer should be $30$ by my book.