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

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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:

$- 1 \leq x - 1 \leq 1$ $-1 <= x - 1 <=1$

Add 1 to all:

$0 \leq x \leq 2 \leftarrow$ $0 <= x <=2 larr$ this is the domain.

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

$0 \leq y \leq π \leftarrow$ $0 <= y <= pi larr$ this is the range.

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

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