AP EAMCET Engineering 26 Apr 2017 Shift 1 Paper

The function is continuous in the interval,
(−∞,1),(1,3),(3,5) and (5,∞)
Check for continuity at x=1.

lim

x→1−1

f(x)=1−1
= 0
And,

lim

x→1+1

f(x)=2−1
=1
So, the function is not continuous at x=1
Check for continuity at x=3

lim

x→3−1

f(x)=2−9
=−7
And,

lim

x→3+

f(x)=3−10
=−7
Therefore, the function is continuous at x=3
Check for continuity at x=5

lim

x→5−

f(x)=5−10
= -5
And,

lim

x→5+

f(x)=2×5
= 10
Thus, the points of discontinuity of f is {1,5}.