State the domain for which the inverse function is decreasing.
Don't really understand this question...
inverse function of y=cosx (which is y=cos^-1(x))
if you look at the unit circle
cosine decreases continuously from zero to π
take a look at the graph. it increases on [-1,1] but you need to restrict the domain of cos(x) to [-π,0] or [π,2π], etc.
oops. my bad. I read "increasing"
To understand this question, let's start with the concept of an inverse function.
An inverse function is a function that "undoes" the actions of another function. For example, if you have a function f(x) that takes an input x and generates an output y, the inverse function f^-1(y) will take that output y and give you the original input x.
Now, when we talk about a function being "decreasing," it means that as the input increases, the output decreases. Conversely, if the input decreases, the output increases.
In the context of the question, we are looking for the domain of the original function where the inverse function is decreasing. This means we want to find the set of input values for which, as we increase those values, the output of the inverse function decreases.
To determine the domain for which the inverse function is decreasing, we need to consider the original function's graph. If we have the graph of the original function, we can visually observe the portions where the function is decreasing. For those portions, the corresponding domain values will give us the answer.
If you don't have the graph, you can try to find this information by analyzing the properties of the original function. For example, if the original function is a linear function with a negative slope, the inverse function will be decreasing for the entire domain. On the other hand, if the original function is not a one-to-one function, meaning it fails the horizontal line test, then the inverse function might not be decreasing over the entire domain.
In summary, to determine the domain for which the inverse function is decreasing, you need to consider the graph or the properties of the original function.