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Questions  

 If f(x) is continuous and increasing function such that  domain of g(x)=f(x)x be R and h(x)=11x, then 

 the domain of ϕ(x)=f(f(f(x)))h(h(h(x))) is 

a
R
b
{0,1}
c
R−{0,1}
d
R−(0,1)

detailed solution

Correct option is C

hx =11-x ,x≠1 ⇒hhx= 11-11-x= x-1x, x≠0,1 ⇒ hhhx=11-x-1x=x , x≠0,1 ⇒gx =fx-x≥0 ,for all x∈R  ⇒  fx≥x ⇒ffx≥fx≥x   since fx is increasing function      ⇒  similarly fffx≥x     ⇒fffx-x ≥0 , for all x∈R-0,1     ⇒ φx  =fffx-x   is defined for all x∈R-0,1

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