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# Function Domain

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How is domain of the function f(x)=cosx restricted so that its inverse function exists?

The domain of f(x)=cosx is restricted to           so that the inverse of the function exists. This means that all functional values of f(x)=cos−1x are on the interval          .

Put answers into each box to correctly complete the statements. There should be 2 answers.

(- pi / 2, pi / 2)     [- pi / 2, pi / 2]     (0, pi)     [0, pi]     (0, 2pi)     [0, 2pi]

I got [- pi / 2, pi / 2] for both statements, but I just want to make sure that I'm right. If you can help me, it would be appreciated!

(Also, if someone could explain what the difference is between the brackets and the parenthesis, that would be wonderful.) Mar 24, 2020
edited by auxiarc  Mar 24, 2020

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Maybe  this will help  :  https://www.desmos.com/calculator/46w8zosudi

The  domain for cos (x)  is  [ 0 ,pi ]

The range   of cos (x)  = [ -1, 1 ]

Then  the domain for  the  inverse cosine  is  [ -1,1]

And  the  functional values  (the range)  for the  inverse cosine  is   [ 0 , pi ]

Parentheses  do not  include the  endpoint(s)  of an interval

Thus   (0, 3)   include all the real numbers  between  0 an 3, but  not including  0  or  3

Brackets include the endpoints....so  [0,3 ]  include  all real numbers between 0 and 3  including  0 and 3

Note  that  these  could  be combined

So   [0, 3)  includes  0  but  not 3  on the interval

And  (0, 3]   includes 3 but not 0  on the interval

One more note :  infinity  is  never bracketed   Mar 24, 2020
edited by CPhill  Mar 24, 2020