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`f(x)={(x-1",",-1 le x le 0),(x^(2)",",0le x le 1):} and g(x)=sinx` Consider the functions `h_(1)(x)=f(|g(x)|) and h_(2)(x)=|f(g(x))|.` Which of the following is not true about `h_(1)(x)`?A. It is a periodic function with period `pi`.B. The range is [0, 1].C. The domain is R.D. None of these |
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Answer» Correct Answer - D `|g(x)|=|sinx|, x in R` `f(|g(x)|)={(|sinx|-1",",-1 le |sinx| lt 0),((|sinx|)^(2)",", 0le (|sinx|) le 1):}=sin^(2)x,x in R` `f(g(x))={(sinx-1",",-1 le sinx lt 0),(sin^(2)x",", 0le sinx le 1):}` `={(sinx-1",",(2n-1) pi lt x lt 2n pi),(sin^(2)x",", 2n pi le x le (2n+1)pi):},n in Z.` 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.` Clearly, `h_(1)(x)=f(|g(x)|)=sin^(2)x` has period `pi`, range [0, 1], and domain R`. |
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