Verify that`x sgnx=|x|``|x|sgnx=x``x(sgnx)(sgnx)=x` – InterviewSolution

1.	Verify that`x sgnx=\|x\|``\|x\|sgnx=x``x(sgnx)(sgnx)=x`
Answer» (i) `x " sgn "x={(x1",",x gt 0),(0",", x=0),(x(-1)",",x lt 0):} = {(x",",x gt0),(0",",x=0),(-x",", x lt 0):}=\|x\|` (ii) `\|x\| " sgn "x={(x1",",x gt 0),(0",", x=0),((-x)(-1)",",x lt 0):} = {(x",",x gt0),(0",",x=0),(x",", x lt 0):}=x` (iii) `x ("sgn "x) ("sgn "x)=\|x\| " sgn " (x)=x`

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