Dewight needs to restrict the domain of the cosine function so that the inverse is a function. Which description best describes how she could restrict the domain?
A) So that y = cos(x) is always decreasing
B) So that y = cos(x) only has one maximum <my choice
C) So that y = cos(x) only has one minimum
D) So that y = cos(x) only has two maximum
nope. If it has a maximum, then the graph turns back on itself, so it fails the horizontal-line test.
so that means it would always be decreasing?
that's right.
To restrict the domain of the cosine function so that the inverse is a function, we need to ensure that each value in the domain maps to a unique value in the range. This means that we need to avoid having any repeated values in the range of the cosine function.
A) Restricting the domain so that y = cos(x) is always decreasing does not guarantee that each value in the domain maps to a unique value in the range. It only ensures that the values in the range are decreasing.
B) Restricting the domain so that y = cos(x) only has one maximum is a valid approach. The cosine function oscillates between -1 and 1, and restricting the domain to a specific interval (e.g., [0, π/2]) would ensure that there is only one maximum value in the range (-1).
C) Restricting the domain so that y = cos(x) only has one minimum does not guarantee that each value in the domain maps to a unique value in the range. It only ensures that the values in the range have a single minimum point.
D) Restricting the domain so that y = cos(x) only has two maximum is not a valid approach. The cosine function has an infinite number of maximum points in its range, so it is not possible to restrict the domain to have only two maximum points.
Therefore, the best description that explains how Dewight could restrict the domain of the cosine function so that the inverse is a function is option B) So that y = cos(x) only has one maximum.