For the inequation (1.25)1−x<(0.64)2(1+√x)
(54)1−x<(1625)2(1+√x) (45)x−1<(45)4(1+√x) Now 0<45<1⇒x−1>4(1+√x) x−4√x−5>0⇒(√x−√5)(√x+1)>0 ⇒√x>5⇒x>25
Examine the applicable of MVT for all three functions.
f(x)=[x] for xϵ[5, 9]
f(x)=[x] for xϵ[−2, 2]
f(x)=1−x2 for xϵ[1, 2]