Inverse Function Homework: Slope of 1/2

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To find all points where the inverse function of f(x) = 2x + cos(x) has a slope of 1/2, it's necessary to determine where the original function has a slope of 2. The calculated x-values of 0, π, and 2π are correct, but the discussion emphasizes that there are infinitely many solutions, represented as nπ, where n is any integer. The conversation highlights the importance of considering all possible points, not just a few specific ones. This approach ensures a comprehensive solution to the homework problem.
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Homework Statement


Hello, this is what the question states:

Consider the function f(x) = 2x + cos(x). Find all points at which the inverse function has a slpe of 1/2.


The Attempt at a Solution


What I did was find where the original function has a slope of 2. Those x values would become the y values for the inverse function. So x would = 0, pi, 2pi.

Is this correct? Enlighten !
 
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That seems right. You have three points. But there are many more, right? Like 3pi, 4pi, -pi, -2pi, etc? The problem did say to find ALL points.
 
Ok, thanks. And you so it would be like n pi.
 

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