Find the Domain f(x)=arccos(x)

Problem

ƒ(x)=arccos(x)

Solution

1. Identify the definition of the inverse cosine function. The function y=arccos(x) is the inverse of the cosine function x=cos(y) restricted to the interval 0≤y≤π

2. Determine the range of the original cosine function. For any real number y the value of cos(y) is always between −1 and 1 inclusive.

3. Apply the property of inverse functions. The domain of an inverse function is equal to the range of the original function.

4. Set the inequality for the domain. Since the range of cos(y) is [−1,1] the input x for arccos(x) must satisfy −1≤x≤1

Final Answer

Domain of *arccos(x)={[x∈ℝ,−1≤x≤1]}

Want more problems? Check here!