InterviewSolution
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InterviewSolution
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find the value of theA. `pm sqrt(npi), n in {0, 1, 2, …. } `B. `pm sqrt(npi ), n in {1, 2, …}`C. `(pi)/(2)+ 2npi, n in {…, - 2, -1, 0, 1 , 2, …}`D. `2n pi, n in {… -2, -1, 0, 1, 2,… }` |
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Answer» Correct Answer - A We have, `f(x) = x^(2) and g (x) = sin x` `therefore (fogogof) (x) = (fog) (gof(x)) =(fog)(g(f(x))) = (fog) = (sin^(2))` `= f(g(sinx^(2)) = f(sin(sin x^(2)) = sin^(2) (sin x^(2))` and, `(gogof) (x) = (gog) (f(x)) = (gog) (x^(2)) = g(g(x^(2))` `therefore (fogogof) (x)= (gofog) (x)` `rArr sin^(2) (sin x^(2)) = sin (sin x^(2))` `rArr sin (sin^(2)) = sin (sins^(2))` `rArr sin (sin x^(2)){ sin (sin x^(2))-1)} = 0` `rArr sin(xin x^(2)) = 0 or, sin (sin x^(2)) = 1` `sin x^(2) = npi, n in Z or, sin x^(2) = 2mpi +(pi)/(2), m in Z` `rArr sin x^(2) = 0` `rArr x^(2) = n pi, n in Z` `rArr = pm sqrt(npi, n in {0,1,2,3,......}` |
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