If f(x)=limt→∞ |a+sin⁡πx|t−1|a+sin⁡πx|t+1,x∈(0,6), then

Given function is discontinuous when a+sin⁡πx=1Now, if a = 1, then sin⁡πx=0 or x=  1, 2,3, 4, 5.If a= 3, then sin⁡πx=−2, not possible.If a = 0.5, then sin⁡πx=0.5.Therefore, x has 6 values, 2 each for one cycle of period2.If a = 0, then sin⁡πx=+1 or x=12,32,52,72,92,112Hence, all the options are correct.