Thread: find the largest possible domain of this function

find the largest possible domain of this function

square root of pi/4-arcosx...everything is under the square root

Originally Posted by domenfrandolic

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square root of pi/4-arcosx...everything is under the square root

Draw the graph of $\displaystyle w = \frac{\pi}{4} - arccos(x)$. The implied domain will be the values of x for which $\displaystyle w \geq 0$.

the problem is i dont know how to do it

The square root is only defined for non-negative numbers so the domain is $\displaystyle \frac{\pi}{4}- arccos(x)> 0$ which is the same as saying that $\displaystyle arccos(x)< \frac{\pi}{4}$. One boundary of that will be where $\displaystyle arccos(x)= \frac{\pi}{4}$ or $\displaystyle x= cos(\pi/4)$. Remember that cosine is a decreasing function.

so the answer is cos(pi/4)?

Do you not understand what a "domain" is? The domain of a functions is a set of numbers, not a single number.

yeah i knew that but like which others are the answers?sorry about that but i am quit stuck with the given function

you should already know what the basic arccos function looks like ...



perform the necessary transformations to obtain the graph of

$\displaystyle y = \frac{\pi}{4} - \arccos{x}$

then determine the interval where $\displaystyle y \ge 0$

Originally Posted by domenfrandolic

yeah i knew that but like which others are the answers?sorry about that but i am quit stuck with the given function

Your problem is that you do not have a sufficient understanding of the pre-requisite mathematical knowledge assumed for this question. I suggest you go back to your class notes or textbook and review inverse trigonometric functions before making further attempts on this question.