InterviewSolution
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InterviewSolution
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The value of `k(k >0)`such that the length of the longest interval in which the function `f(x)=sin^(-1)|sink x|+cos^(-1)(cosk x)`is constant is `pi/4`is/ are8 (b) 4(c) 12 (d)16A. 8B. 4C. 12D. 16 |
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Answer» Correct Answer - B `f(x) = sin^(-1) |sin kx| + cos^(-1) (cos kx)` Let `g(x) = sin^(-1) |sin x| + cos^(-1) (cos x)` `g(x){(2x,0 le x le(pi)/(2)),(pi,(pi)/(2) lt x le (3pi)/(2)),(4pi - 2x,(3pi)/(2) lt x le 2pi):}` `g(x)` is periodic with period `2pi` and is constant in the continuous interval `[2n pi + (pi)/(2), 2n pi + (3pi)/(2)] ("where " n in I) and f(x) = g(kx)`. So, `f(x)` is constant in the interval `[(2npi)/(k) + (pi)/(2k), (2n pi)/(k) + (3pi)/(2k)]` Thus, `(pi)/(4) = (3pi)/(2k) -(pi)/(2k)` or `(pi)/(k) = (pi)/(4)` or `k = 4` |
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