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If f(x)={{:(,|x|, x le1),(,2-x,x gt 1):}...

If `f(x)={{:(,|x|, x le1),(,2-x,x gt 1):}`, then fof (x) is equal to

A

`f(x)={{:(,2-x,x lt -1),(,|x|, -1 le x le 1),(,|2-x|,x gt 1):}`

B

`f(x)={{:(,|x|, x lt -1),(,2-|x|,-1le x le 1),(,|2-x|,x gt 1):}`

C

`f(x)={{:(,|2-x|,x lt -1),(,|x|, -1 le x le 1),(,2-|x|,x gt 1):}`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`fof(x)=f(f(x))`
`Rightarrow fof(x)={{:(,f(|x|),x le1),(,f(2-x),x gt 1):}`
`Rightarrow fof(x)={{:(,||x||,"if"-1 le x le 1),(,2-|x|,"if"x lt -1),(,|2-x|,"if"x gt 1"):}`
`Rightarrow fof(x)={{:(,|x|,"if"-1 le x le 1),(,2-|x|,"if " x lt -1),(,|2-x|,"if "x gt 1):}`
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