# Inverse Function Homework: Slope of 1/2

• jordan123
In summary, the question is asking to find the points at which the inverse function of f(x) = 2x + cos(x) has a slope of 1/2. The solution involves finding the points where the original function has a slope of 2, which would become the y values for the inverse function. The correct points are n*pi, where n is any integer.
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 !

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.

## 1. What is an inverse function?

An inverse function is a mathematical operation that reverses the effect of another function. It is denoted by f-1 and is used to find the original input when given the output of a function.

## 2. How is the slope of 1/2 related to inverse functions?

The slope of 1/2 is a common characteristic of inverse functions. It indicates that for every unit change in the input of the inverse function, the output changes by 1/2 of a unit. This slope is also known as the "half-angle" slope and is a key factor in solving equations involving inverse functions.

## 3. Can you give an example of an inverse function with a slope of 1/2?

One example of an inverse function with a slope of 1/2 is f(x) = 2x + 3. The inverse of this function is f-1(x) = (x - 3)/2. The slope of this inverse function is 1/2, as for every unit change in x, the output changes by 1/2 of a unit.

## 4. How can I find the inverse of a function with a slope of 1/2?

To find the inverse of a function with a slope of 1/2, you can use the general method of finding inverse functions. This involves switching the x and y variables in the function and then solving for y. The resulting equation will be the inverse function with a slope of 1/2.

## 5. What are some real-life applications of inverse functions with a slope of 1/2?

Inverse functions with a slope of 1/2 are commonly used in physics and engineering, specifically in problems involving motion and velocity. For example, the inverse function of velocity (meters per second) with a slope of 1/2 would give the time (in seconds) it takes for an object to travel a certain distance. These functions are also used in finance and economics to calculate growth rates and interest rates.

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