Domain and Range

Question

Hello. I'm having a little trouble finding the range of a function. The function is f(x) = arccos(x). I found that the domain is [-1,1] but I'm having a little trouble finding the range. I know that the range is [0,x], but I can't find x. x isn't infinity either as I tried. Thank you for help.

Answer 1

The arccosine function is the inverse function of y = cosx, where 0 ≤ x ≤ π ( We restrict the domain of cosine to the interval [0,π] so that we get a one to one function).  

 

So, the restricted cosine has domain [0, π].

 

domain f = range f^-1.

 

Therefore, the range of arccosx is [0, π].