Inverse Function Homework: Slope of 1/2

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SUMMARY

The discussion centers on finding all points where the inverse function of f(x) = 2x + cos(x) has a slope of 1/2. The correct approach involves determining where the original function has a slope of 2, leading to the conclusion that the x-values corresponding to these slopes are 0, π, 2π, and all integer multiples of π (nπ). This method confirms that the inverse function's slope condition is satisfied at these points.

PREREQUISITES
  • Understanding of inverse functions
  • Knowledge of derivatives and slopes
  • Familiarity with trigonometric functions
  • Basic calculus concepts
NEXT STEPS
  • Study the properties of inverse functions in calculus
  • Learn how to compute derivatives of composite functions
  • Explore the implications of slopes in inverse functions
  • Review trigonometric identities and their applications in calculus
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Students studying calculus, particularly those focusing on inverse functions and derivatives, as well as educators seeking to clarify concepts related to slopes in mathematical functions.

jordan123
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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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