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?
So that y = cos(x) is always decreasing
So that y = cos(x) only has one maximum
So that y = cos(x) only has one minimum
So that y = cos(x) only has two maximum
I chose B
Still no. try (A)
If there is a min or max, the curve folds back on itself, so it is no longer invertible. It fails the horizontal line test.
To answer this question, let's consider the key characteristics of the cosine function and its inverse.
The cosine function, y = cos(x), has a periodic nature, oscillating between values of -1 and +1. It repeats itself every 2π units in the x-axis.
The inverse of the cosine function, also known as the arccosine function or cos^(-1)(x), is the reflection of the cosine function across the line y = x. The domain of the inverse function is restricted to a certain subset of the original cosine function's range in order to obtain a single-valued function.
Considering these characteristics, let's analyze each option:
A) Restricting the domain so that y = cos(x) is always decreasing: This is not the correct answer because the cosine function is not always decreasing. It oscillates between increasing and decreasing values, so restricting the domain based on this criterion would not guarantee a single-valued inverse function.
B) Restricting the domain so that y = cos(x) only has one maximum: This is indeed the correct answer. By restricting the domain of the cosine function so that it only includes one maximum value, we ensure that no x-value repeats for a given different y-value. As a result, the inverse function will be a single-valued function.
C) Restricting the domain so that y = cos(x) only has one minimum: This is not the correct answer because the cosine function has infinitely many minimum values, occurring every 2π units in the x-axis. Restricting the domain based on this criterion would not guarantee a single-valued inverse function.
D) Restricting the domain so that y = cos(x) only has two maxima: This is not the correct answer because the cosine function has infinitely many maximum values, occurring every 2π units in the x-axis. Restricting the domain based on this criterion would not guarantee a single-valued inverse function.
Therefore, the correct answer is B) Restricting the domain so that y = cos(x) only has one maximum.