Finding Domain & Range

**Paymemoney** · January 14th 2010, 03:35 PM

Hi
How would you find the domain and range of $cos^{-1}(x^2)$ if the domain of cos(x) is restricted to $[0,\pi]$ .

P.S

**Grandad** · January 14th 2010, 10:03 PM

Hello Paymemoney

Originally Posted by Paymemoney

Hi
How would you find the domain and range of $cos^{-1}(x^2)$ if the domain of cos(x) is restricted to $[0,\pi]$ .

P.S

Edited version: second thoughts about my first answer.

In Britain, the inverse cosine function is almost always written as $\cos^{-1}$ , whereas $\arccos$ is widely used elsewhere. Since I posted my original answer, it occurred to me that I interpreted $\cos^{-1}(x^2)$ as the inverse cosine of $x^2$ , whereas the question might mean $\Big(\cos(x^2)\Big)^{-1} =\frac{1}{\cos(x^2)}$ . Also, I am not clear how the domain of $\cos(x)$ being restricted to $[0,\pi]$ is relevant.

So, unless someone can clarify what the question means, I'll keep quiet!

Grandad

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