find the largest possible domain of this function
square root of pi/4-arcosx...everything is under the square root
find the largest possible domain of this function
square root of pi/4-arcosx...everything is under the square root
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.
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.