InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Consider the function `f(x) = sin^(-1)x`, having principal value branch `[(pi)/(2), (3pi)/(2)] and g(x) = cos^(-1)x`, having principal value brach `[0, pi]` The value of `f(sin 10)` isA. `10 - 3pi`B. `10 -2 pi`C. `10 -(5pi)/(2)`D. `(7pi)/(2) - 10` |
|
Answer» Correct Answer - B We have `f(x) = sin^(-1)x`, having range `[(pi)/(2), (3pi)/(2)]` Consider the function `h(x) = (pi - sin^(-1) x)`, where `sin^(-1) x in [-(pi)/(2), (pi)/(2)]` Clearly, function `f(x) and h(x)` are identical. Advantage with function `y = h(x)` is that we are well versed with `sin^(-1) x` if `(sin^(-1) x) in [-(pi)/(2), (pi)/(2)]` `h(sin 10) = pi - sin^(-1) (sin 10)` `= pi - sin^(-1) (sin (3pi - 10)))` `= pi - (3pi - 10)` `= 10 - 2pi` Now, `f(x) lt (3pi)/(4)` `:. h(x) lt (3pi)/(4)` `rArr pi - sin^(-1) x lt (3pi)/(4)` `rArr sin^(-1) x gt (pi)/(4)` `rArr (pi)/(4) lt sin^(-1) x le (pi)/(2)` `rArr (1)/(sqrt2) lt x le 1` |
|