Inverse Function Homework: Slope of 1/2

[jordan123]

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 !

 

[Dick]

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.

 

[jordan123]

Ok, thanks. And you so it would be like n pi.