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Which of the following functions is/are identical to `|x-2|` ? (a) `f(x)=sqrt(x^(2)-4x+4) " (b) " g(x)=|x|-|2|` (c ) `h(x)=(|x-2|^(2))/(|x-2|) " (d) "t(x)=|(x^(2)-x-2)/(x+1)|` |
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Answer» Correct Answer - a `f(x)=sqrt(x^(2)-4x+4)=sqrt((x-2)^(2))=|x-2|` `g(x)=|x|-|2|=|x|-2=={(-x-2",",x lt 2),(x-2",",x ge2):}`. Thus `g(x)` is not same as `|x-2|` `h(x)=(|h-2|^(2))/(|x-2|)=|x-2|,x ne 2.` This is not same as `|x-2|` as `h(x)` has domain `R-{2}` `t(x)=|(x^(2)-x-2)/(x+1)|=|((x-2)(x+1))/(x+1)|=|x-2|, x ne -1`. Thus `t(x)` is not same as `|x-2|` as `t(x)` has domain `R-{-1}.` |
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