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

Answer

Domain:
Range: `{pi//4,3pi//4}`

Explanation

We have `f(x)=sin^(-1)x +tan^(-1)x +sec^(-1)x`
Domain of `sin^(-1)x " is " [-1,1].`
Domain of `tan^(-1)x ` is R.
Domain of `sec^(-1)x " is " R-(-1,1)`
So, domain `f(x) " is " {-1,1}`
`f(-1)=sin^(-1)(-1)+tan^(-1)(-1)+sec^(-1)(-1)`
` = -pi//2-pi//4+pi=pi//4`
` f(1)=sin^(-1)(1)+tan^(-1)(1)+sec^(-1)(-1)`
`= pi//2+pi//4+0=3pi//4`
Hence range is `{pi//4,3pi//4}`