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Let f(x)=max{1+sinx,1,1-cosx}, xin[0,2pi...

Let `f(x)=max{1+sinx,1,1-cosx}, xin[0,2pi] and g(x)=max{1,|x-1|} x in R`, then

A

`g(f(0))=1`

B

`g(f(1))=1`

C

`f(f(1))=1`

D

`f(g(0))=1+sin 1`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`f(0)=max {1+sin 0,1,1-cos 0}=1`
`g(0)=max{1,|0-1|}=1`
`f(1)=max [1+sin1,1,1-cos1}=1+sin1`
`g(f(0))=g(1)=max{1,|1-1|}=1`
`f(g(0))=f(1)=1+sin1`
`g(f(1))=g(1+sin1)=max{1,|1+sin1-1|}=1`
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