Find the Domain arccos(x)

Problem

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. Determine the range of the original cosine function, which is the set of all possible output values [−1,1]

3. Apply the property that the domain of an inverse function is equal to the range of the original restricted function.

4. Conclude that for arccos(x) to be defined, the input x must fall within the interval [−1,1]

Final Answer

Domain of *arccos(x)={[x∈ℝ,−1≤x≤1]}

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