is continuous in [0,∞) ⇒continuous at x=1 and x=√2
Lim
x→1−
f(x)=
Lim
x→1+
f(x)=f(1) ⇒
2
a
=a⇒a2=2.......(1) and
Lim
x→√2−
f(x)=
Lim
x→√2+
f(x)=f(√2) ⇒a=
2b2−4b
2√2
⇒b2−2b=√2a If a=√2 then b2−2b−2=0⇒b=1±√3 If a=−√2 then b2−2b+2=0⇒ b is imaginary which is not possible ⇒(a,b)=(√2,1+√3) or (√2,1−√3)