f(x)=(⌊a⌋2−5⌊a⌋+4)x3−(6{a}2−5{a}+1)x−(tan(x))sgn(x)
Provided that f(x) be an even function for all x∈R. If sum of all possible values of a is QP for coprime positive integers P,Q, then find the value of (P+Q).
Details And Assumptions:
⌊..⌋ is floor function or greatest integer function.
{..} is fractional part function.
sgn(x) is signum function defined as : sgn(x)=⎩⎪⎨⎪⎧1,x>00,x=0−1,x<0.