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If the domain of `y=f(x)i s[-3,2],`then find the domain of `g(x)=f(|[x]|),w h e r[]`denotes the greatest integer function. |
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Answer» Correct Answer - [-2, 3) Here, `f(x)` is defined for `x in [-3,2].` For `g(x)=f(|[x]|)` to be defined, we must have `-3 le |[x]| le 2` or `0le |[x]| le 2 " " ["As" |x| ge 0 " for all " x]` or ` -2 le [x] le 2 " " ["As " |x| le a implies-a le x le a]` or `-2 le x lt 3 " " ` [By the definition of greatest integral function] Hence, domain of `g(x)` is `[-2,3)`. |
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