Find the Domain y=arccos(x)

Problem

y=arccos(x)

Solution

1. Identify the definition of the inverse cosine function, y=arccos(x) which is the inverse of the function ƒ(x)=cos(x) restricted to the interval [0,π]

2. Recall that the domain of an inverse function is the range of the original function.

3. Determine the range of the cosine function, ƒ(x)=cos(x) which is the interval [−1,1]

4. Conclude that the input x for arccos(x) must satisfy the inequality −1≤x≤1

Final Answer

Domain: *[−1,1]

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