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Find the range of the following (i) f...

Find the range of the following
(i) `f(x)="sgn"(x^(2)) " (ii) "f(x)="sgn"(x^(2)-2x+3)`

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(i) We know that `x^(2) ge 0 AA x in R`
` :. "sgn"(x^(2))={(0",",x^(2)=0),(1",",x^(2) ne 0):}={(0",",x=0),(1",",x ne 0):}`
Hence range of f(x) is `{0,1}`
(ii) ` x^(2)-2x+3=(x-1)^(2)+2gt 0 AA x in R.`
So, `f(x)= "sgn" (x^(2)-2x+3)=1`
Hence, range of f(x) is `{1}`
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