AP EAMCET Engineering 20 Apr 2019 Shift 1 Paper

Consider the function
f(x)=[

5	‌	‌if ‌x≤1
a+bx	‌	‌ if ‌1<x<3
b+5x	‌	‌ if ‌3≤x<5
30	‌	‌ if ‌x≥5.

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