How to square a piecewise function? :/

So, in summary, to square a piecewise function, you need to square each part separately and then combine the results.
  • #1
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how to square a piecewise function? urgent :/

Homework Statement


square the following piecewise function
f(x)= 0 [-pi,-pi/2)
pi [-pi/2,pi/2)
0 [pi/2,pi)

Homework Equations


N/A


The Attempt at a Solution


so i think this is how you do it:
(0)2 + (pi)2 +(0)2 is this ocrrect?

or is it the following:

(0+pi+0)2? I am so lost:/

( I am trying to find the energy of the kth harmonic so i need to square the function first) :/

thanks in advance
BA
 
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  • #2


Why do you expect that the square of a piecewise function has the same value everywhere?

You just need to calculate f(x)² which can give different values depending on what x is.
 
1.

What is a piecewise function and why do we need to square it?

A piecewise function is a function that is defined by different equations or rules for different parts of its domain. Squaring a piecewise function is a common mathematical operation that helps simplify the function or make it easier to work with in certain situations.

2.

How do you square a piecewise function with multiple pieces?

To square a piecewise function with multiple pieces, you can square each individual piece separately and then combine them back together. Alternatively, you can use the distributive property to expand the squared function and then simplify it based on the pieces of the original function.

3.

Can you square a piecewise function with non-integer exponents?

Yes, you can square a piecewise function with non-integer exponents by using the rules of exponents. For example, a piecewise function with an exponent of 1/2 would be squared by raising each piece to the power of 1/2 and then combining them back together.

4.

Are there any special cases to consider when squaring a piecewise function?

Yes, there are a few special cases to consider when squaring a piecewise function. One case is when the function has a negative value, in which case the squared function may have multiple solutions. Another case is when the function has a piece with a negative coefficient, which can affect the overall shape of the squared function.

5.

What are some real-life applications of squaring a piecewise function?

Squaring a piecewise function can be useful in various fields such as physics, engineering, and economics. For example, it can be used to model the relationship between two variables with non-linear behavior, or to approximate complex functions with simpler ones. It can also be used in optimization problems to find the maximum or minimum value of a function with multiple pieces.

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