Let-f-x-cos-1-x-cos-1-x-1-find-the-range-of-f-

Question Number 136186 by ZiYangLee last updated on 19/Mar/21

Let f (x) = \cos^{- 1} x + \cos^{- 1} (x - 1),

find the range of f .

Answered by ZiYangLee last updated on 19/Mar/21

Ans : [\frac{π}{2}, \frac{3 π}{2}]

Answered by MJS_new last updated on 19/Mar/21

f (x) is defined for 0 ⩽ x ⩽ 1 and is strictly

monotonically decreasing

\Rightarrow

f (1) ⩽ f (x) ⩽ f (0) \Leftrightarrow \frac{π}{2} ⩽ f (x) ⩽ \frac{3 π}{2}

Commented by ZiYangLee last updated on 20/Mar/21

thanks