ƒ(x) can't be constant throughout the domain. Hence we can find x∊(r,s) such that ƒ(x) is one-one option (A) is true Option (B):
|f1(x0)|=|
f(0)−f(−4)
4
|≤1(LMVT)
Option (C): f(x)=sin(√85x) satisfies given condition But
lim
x→∞
sin(√85x)D.N.E⇒Incorrect Option (D): g(x)=f2(x)+(f1(x))2 |f1(x1)≤1| (by LMVT) |f(x1)|≤2 (given) ⇒g(x1)≤5∃x1∈(−4,0) Similarly g(x2)≤5∃x2∊(0,4) g(0)=85⇒g(x) has maxima in (x1,x2) say at α g1(α)=0 and