UPSC NDA I 2015 Mathematics Solved Paper

For the given function to be continuous on R, left hand limit should be equal to right hand limit at 0 and 1.
Therefore

lim

x→0+

f(x)

lim

x→0+

(ax+b)
=b

lim

x→0+

f(x)
=

lim

x→0+

(−1)
=−1
LHL = RHL
b=−1
Similarly applying for x = 1 we get

lim

x→1−

f(x)

lim

x→1+

(ax+b)
=a+b

lim

x→1+

f(x)
=1
LHL = RHL
a+b=1
a+(−1)=1
a=2