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Domain of `h_(1)(x) and h_(2)(x)" is " x in [2n pi,(2n+1)pi],n in Z.`Range of `h_(1)(x) and h_(2)(x)" is " [0,1]`Period of `h_(1)(x) and h_(2)(x) " is " pi`None of these

Answer :

CSolution :

`|g(x)|=|sinx|, x in R` <br> `f(|g(x)|)={(|sinx|-1",",-1 le |sinx| lt 0),((|sinx|)^(2)",", 0le (|sinx|) le 1):}=sin^(2)x,x in R` <br> `f(g(x))={(sinx-1",",-1 le sinx lt 0),(sin^(2)x",", 0le sinx le 1):}` <br> `={(sinx-1",",(2n-1) pi lt x lt 2n pi),(sin^(2)x",", 2n pi le x le (2n+1)pi):},n in Z.` <br> or `|f(g(x))|={(sinx-1",",(2n-1) pi lt x lt 2n pi),(sin^(2)x",", 2n pi le x le (2n+1)pi):},n in Z.` <br> For `h_(1)(x)-=h_(2)(x)=sin^(2)x, x in [2n pi,(2n+1) pi], n in Z,` and has range [0, 1] for the common domain. <br> Also, the period is `2pi` (from the graph).