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If f(x)=|x-2|" and "g(x)=f(f(x)), then f...

If `f(x)=|x-2|" and "g(x)=f(f(x)),` then for `2ltxlt4,g'(x)` equals

A

-1

B

1

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`f(x)={{:(x-2" ,"," for "4gtxge2),(-(x-2)","," for "xlt2):}`
`g(x)=f(f(x))`
`impliesg(x)={{:(f(x-2)" ,"," for "2lexlt4),(f(-(x-2))","," for "xlt2):}`
`impliesg(x)={{:(-(x-2-2)" ,"," for "2lexlt4),(-(-x+2-2)","," for "0ltxlt2):}`
`impliesg'(x)={{:(-1",",ltxlt4),(1" ,",0ltxlt2):}`
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OBJECTIVE RD SHARMA-DIFFERENTIATION-Section I - Solved Mcqs
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