f(x)={x−1,−1≤x<0x2,0≤x≤1 and g(x)=sinx. Consider the function h1(x)=f(|g(x)|) and h2(x)=|f(g(x))| For when h1(x) and h2(x) are identical functions, then which of the following is not true?
A
Domain of h1(x) and h2(x) is [2nπ,(2n+1)π],n∈Z
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B
Range of h1(x) and h2(x) is [0,1]
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C
Period of h1(x) and h2(x) is π
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D
None of these
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Solution
The correct option is C Period of h1(x) and h2(x) is π |g(x)|=|sinx|,∀x∈R f(|g(x)|)={|sinx|−1,−1≤|sinx|<0(|sinx|)2,0≤|sinx|≤1⇒h1(x)=f(|g(x)|)=sin2x