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`if y=tan^(-1)x+"tan"^(-1)(1)/(x)+sec^(-1)x,then" "yin`A. `[(pi)/(2),pi)uu(pi,(3pi)/(2)]`B. `[(pi)/(2),(3pi)/(2)]`C. `(o,pi)`D. `[o,(pi)/(2))uu[(pi)/(2),pi)` |
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Answer» Correct Answer - 3 `therefore` Domain is x`in(-oo,-1]cup[1,oo)` case(1):`x ge1`, `y=tan^(-1)x+ tan^(-1)""(1)/(x)+sec^(-1)x` `=(pi)/(2)+sec^(-1)xforall sec^(-1)x in[0,(pi)/(2))y in[(pi)/(2),pi)` case(2), `xle-1,y=tan^(-1)x+tan^(-1)""(1)/(x)+sec^(-1)x` `tan^(-1)x+cot^(-1)x-pi+sec^(-1)x` `=sec^(-1)-(pi)/(2) forallsec^(-1)x in((pi)/(2),pi]` so `y in (o,(pi)/(2)]` `therefore y in (o,pi)` |
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