If fx=sgnx2-ax+1 has maximum number of points of discontinuity then
a∈2,∞
a∈-∞,-2
a∈-2,2
none of these
For maximum points of discontinuity of
fx=sgnx2-ax+1
x2-ax+1=0 must have two distinct roots, for which
D=a2-4>0
or a∈-∞,-2∪2,∞