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

$$\mathrm{Let}f\left(x\right)={\cos }^{-1}x+{\cos }^{-1}(x-1),$$$$\mathrm{find}\mathrm{the}\mathrm{range}\mathrm{of}f.$$

Answered by ZiYangLee last updated on 19/Mar/21

$$\mathrm{Ans}:[\frac{\pi }{2},\frac{3\pi }{2}]$$

Answered by MJS_new last updated on 19/Mar/21

$$f\left(x\right)\mathrm{is}\mathrm{defined}\mathrm{for}0⩽x⩽1\mathrm{and}\mathrm{is}\mathrm{strictly}$$$$\mathrm{monotonically}\mathrm{decreasing}$$$$\Rightarrow$$$$f\left(1\right)⩽f\left(x\right)⩽f\left(0\right)\iff \frac{\pi }{2}⩽f\left(x\right)⩽\frac{3\pi }{2}$$

Commented by ZiYangLee last updated on 20/Mar/21

$$\mathrm{thanks}$$

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