Saved Bookmarks
| 1. |
Find the range of `f(x) = cos^(-1) x + cot^(-1) x` |
|
Answer» Correct Answer - `[(pi)/(4), (7pi)/(4)]` We have `f(x) = cos^(-1) x + cot^(-1) x` Clearly, domain of the function is `[-1 ,1]` Now, both `cos^(-1) x and cot^(-1) x` are decreasing function `:.` f(x) is also decreasing function `:.` Range of the function is `[f (1), f(-1)]` Now, `f(-1) = cos^(-1) + cot^(-1) (-1) = pi + 3 pi//4 = 7 pi//4` `f(1) = cos^(-1) (1) + cot^(-1) (1) = 0 + pi//4 = pi//4` Hence, range is `[pi//4, 7pi//4]` |
|