What is the domain and range of #cos^-1(tanh x)#?

1 Answer
Douglas K.
May 17, 2017

The domain is #x in RR# the range is #y in RR: 0 < y < pi#

Explanation:

The domain of the #tanh(x)# function is any real number: #x in RR#

The range of the #tanh(x)# function is #y in RR: -1 < y < 1#; this does not exceed the domain of the #cos^-1(x)# function but it will never be able to force it to the values #0 and pi#.

Therefore, the range of is : #y in RR: 0 < y < pi#

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