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Find the range of f(x)=sin^(-1)x+tan^(-1...

Find the range of `f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot`

Text Solution

Verified by Experts

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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