(i)For what values of x is sin-1xdefined? (ii)Find the maximum value of 2x(1−x). (iii)Find the range of the function f givenby f(x)=sin-12x(1−x) with domain0≤x≤1.
(i) sin-1 x defined for -1≤x≤1 (ii) Max value of 2x(1-x) occurs when x=12 2(12)(1-12)=12 :. Max xvalue =12 (iii) f(x)=sin-12x(1-x) in 0≤x≤1 normal range od sin-1: -π2≤sin-1≤π2 but for 0≤x≤1 : 0≤sin-1≤π2 But max value of 2x(1-x)=12 :.sin-1(12)=π6 sin-1(0)=0 0≤sin-1 2x(1-x)≤π6
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