# Solving Piecewise Functions in C_p (0, pi) and C ' _p (0, pi)

• jaejoon89
In summary, the question is asking which functions, f(x), g(x), and h(x), are in C_p (0, pi) and/or in C ' _p (0, pi). C_p means "piecewise continuous," but the meaning of C ' _p is unclear. After discussing and researching, it is determined that C ' _p could possibly mean differentiable or piecewise differentiable.
jaejoon89

## Homework Statement

Which are in C_p (0, pi) and/or in C ' _p (0, pi)?

f(x) = {x if 0 < x < pi/2, pi-x if pi/2 < x < pi
g(x) = {sqrt(x) if 0 < x < pi/3, (pi-x)^2 if pi/3 < x < pi
h(x) = {x if 0 < x < pi/2, ln(pi-x) if pi/2 < x < pi

## Homework Equations

(see equations above)

## The Attempt at a Solution

I know C_p means "piecewise continuous" but what is C ' _p? How do you do these? I've been racking my brain on this, am completely lost.

If you know what piecewise continuous is, that's good. Which are? I have no clue what C'_p means. Can you look it up and tell us?

I looked in my book and lecture notes - they don't say!

Then you have perfect justification for not answering the question. Seek clarification. Do you think it might mean differentiable?

Or maybe piecewise differentiable

That would be my guess.

## 1. What is a piecewise function?

A piecewise function is a mathematical function that is defined by different equations on different intervals. It is typically used to model situations where the relationship between variables changes at certain points.

## 2. What is C_p (0, pi) and C ' _p (0, pi)?

C_p (0, pi) and C ' _p (0, pi) refer to the set of continuous and differentiable functions, respectively, on the interval (0, pi). This means that the functions have no breaks or gaps and can be graphed without lifting the pen.

## 3. How do you solve a piecewise function in C_p (0, pi)?

To solve a piecewise function in C_p (0, pi), you need to evaluate each equation separately for the specified interval and then combine the results. Make sure to check the continuity of the function at the endpoints to ensure a smooth transition between the different equations.

## 4. What is the importance of solving piecewise functions in C_p (0, pi)?

Solving piecewise functions in C_p (0, pi) allows us to accurately model and analyze real-world situations where the relationship between variables changes at specific points. It also helps us to better understand the behavior and properties of functions.

## 5. Can you provide an example of solving a piecewise function in C_p (0, pi)?

Sure, here's an example: f(x) = { 2x, x < 1; 3x - 1, 1 ≤ x < 2; x^2, x ≥ 2 }. To solve this piecewise function in C_p (0, pi), we would evaluate 2x when x is less than 1, 3x - 1 when x is between 1 and 2, and x^2 when x is greater than or equal to 2. Then we would combine the results to get the final function f(x).

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