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Find the range of `f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot` |
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Answer» Clearly, the domain of the function is `[-1,1].` Also `tan^(-1)x in [-(pi)/(4),(pi)/(4)] " for " x in [-1,1]` Now, `sin^(-1)x+cos^(-1)x =(pi)/(2)" for " x in [-1,1]` Thus, `f(x)=tan^(-1)x+(pi)/(2), " where " x in [-1,1]` Hence, the range is `[-(pi)/(4)+(pi)/(2),(pi)/(4)+(pi)/(2)]-=[(pi)/(4),(3pi)/(4)]` |
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