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Find the domain and range of `f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x.` |
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Answer» Correct Answer - Domain: Range: `{pi//4,3pi//4}` 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}` |
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