If f(x) is continuous at x=1 then a+b=5‌‌‌......(I) If continuous at x=3 then a+3b=b+15 a+2b=15‌‌‌......(II) If continuous at x=5 then b+25=30 b=5 Substitute 5 for b in equation (II) a+2(5)‌‌=15 a‌‌=5 But equation (I) is not satisfied by a=5 and b=5 then, f:R→R is not continuous for any value of a and b