Question

Use interval notation to represent the domain and range of the following functions. hint: start by thinking about the meaning of each function's input and output quantities and the values those quantities can assume. Determine the domain and range of the cos⁻¹ function

domain =
range =

Answer 1

The domain of the cos⁻¹ function is [-1, 1], and its range is [0, π], since these are the sets of valid input and output values respectively represented in interval notation.

Step-by-step explanation:

Determining the Domain and Range of the cos⁻¹ Function

To use interval notation to represent the domain and range of the cos⁻¹ function, we must understand what inputs (domain) and outputs (range) the function can accept. The cos⁻¹ function, also known as the arccosine function, gives us the angle whose cosine is a given number. So, the domain of the cos⁻¹ function consists of real numbers from -1 to 1, inclusive, because the cosine of an angle cannot be less than -1 or greater than +1.


This is represented in interval notation as [-1, 1]. Meanwhile, the range of the cos⁻¹ function is the set of possible angles it can output, which in radians is between 0 and π (inclusive). So the range in interval notation is [0, π]. Therefore, for the cos⁻¹ function, we have:

Domain = [-1, 1]
Range = [0, π]