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

Problem

ƒ(x)=arcsin(x)

Solution

1. Identify the definition of the inverse sine function, y=arcsin(x) which is the inverse of the sine function x=sin(y)

2. Recall the range of the sine function, x=sin(y) which is the set of all possible output values for x

3. Determine that for any real angle y the value of sin(y) is always between −1 and 1 inclusive.

4. Apply the property that the range of a function is the domain of its inverse function.

5. Conclude that the input x for arcsin(x) must satisfy the inequality −1≤x≤1

Final Answer

Domain of *arcsin(x)=[−1,1]

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