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

Explanation

Solution

Correct option is B)

Given `f(x)=sin ^-1(x)+cos ^-1(x)+tan ^-1(x) `

First we will calculate domain of function f(x) function `sin ^-1(x)` is defined in x in`[-1,1]`

Similarly function `cos ^-1(x)` is defined in x in `[-1,1]` and function `tan ^-1(x)` is defined in x in`(-infty,+infty)`

So` f(x)=sin ^-1(x)+cos ^-1(x)+tan ^-1(x)` is defined in x in[-1,1]

So` f(x)=sin ^-1(x)+cos ^-1(x)+tan ^-1(x)` is defined in x in[-1,1]

So `f(x)=frac(pi)/2+tan ^-1(x)`

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