So, we need to find where is the restriction of to and is the characteristic function of defined by
Do you understand this definition of ? This is a so-called piecewise-defined function. Can you find , , , , ? What are all possible values of ?
This is from a a question i posted a while back but never got a good response to.
"Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=(2,5]."
now another question is find f|A composite XB (big with with subscript B)
My teacher showed the graph for it. But i dont understand it.
Could someone please help in how this graphs comes to be?? Thanks.
So, we need to find where is the restriction of to and is the characteristic function of defined by
Do you understand this definition of ? This is a so-called piecewise-defined function. Can you find , , , , ? What are all possible values of ?
I am genuinely curious about what you don't understand. First note that when I write
is being defined. The meaning of is not composed of the meanings of and , as if you are supposed to know them already. No, one can replace by some symbol , and this would be a definition of a new function .
Could you explain how it is possible to understand the definition of a function and the graph of a function but not understand how to apply the function to a specific value? Do you understand the general concept of a function? Could you be more specific about what you do and do not understand?
I think its the whole concept of the characteristic function. it's only mentioned in a brief paragraph in our book. There really isn't any reasoning behind it. Our teacher didn't explain the purpose of what this is applied too, just decided give a question over it. So i don't know what to do when given this question. I hardly understand the notation. Thanks anyway guys .
The composition can be described by the following situation. Suppose you are a supervisor and you want to meet with your team. You decide do hold two meetings. You give each team member a paper slip with either 0 or 1 written on it. Then you tell everybody that if they get a slip with x written on it, they should come to the meeting at 2 - 3x pm. So, those with 1 come at 2 - 3(1) = -1 pm (let's agree that this is 11 am) and the rest come at 2 pm.
Let B be the group that received 1. The function that for each person returns 0 or 1 is called the characteristic function of the group B; it sets apart people in B by saying that each person in that group received 1. The composition is analogous to a function that, given a person, returns the time of the meeting.
Another minor note: function composition (unfortunately) works in reverse. So you take a real number and plug it into the characteristic function for B before plugging the result into f. Since the range of B is {0, 1} and this lies in the domain of f|A, the function is defined everywhere on R. If A were instead, say, (0, 5], instead of taking value -1 in the range (2, 5] and 2 elsewhere, it would take value -1 in the range (2, 5] and be undefined elsewhere.