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

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

`g(f(0))=1`

`g(f(1))=1`

`f(g(1))=1+sin1`

`f(g(0))=1+sin1`

Text Solution

Verified by Experts

The correct Answer is:

A, B, C, D

`f(x)={{:(1+sinx,0lexle3pi//4),(1-cosx,3pi//4lexle3pi//2),(1,3pi//2lexle2pi):}`
`g(x)={{:(1-x,xle0),(1,0lexle2),(1-1,xle2):}`
`f(0)=1impliesg(f(0))=1`
`f(1)=1+sin1`
`because0lt1lt(3pi)/(4)`
`impliesf(f(1))=1` `because1lt1+sin1lt2`
Again `g(1)=1impliesf(g(1))=1+sin1`
`g(0)=1impliesf(g(0))=1+sin1`

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