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.)
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