What is the domain and range of #arccos(x-1)#?

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Answer 1 · 2017-10-15T22:29:41

The argument of the inverse cosine function must be between the numbers -1 and 1, inclusive, therefore, , one must solve the inequality:

#-1 <= x - 1 <=1#

Add 1 to all:

#0 <= x <=2 larr# this is the domain.

The range the inverse cosine function will only return values within the range:

#0 <= y <= pi larr# this is the range.

It is up to the user to compensate for quadrants other than 1 or 2.