Characteristic Function on A

Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=(2,5].

a.)Sketch the graph of XA•XB

(which has X with an A subscript and X with B subscript, i suppose means XA composite XB)

b.)Sketch the graph f|A•IB

Now i know how to graph XA and XB but im not sure what to do with a.) and i dont know what b.) is even asking.

Any help or suggestions. Much appreciated.

Re: Characteristic Function on A

Quote:

Originally Posted by

**Aquameatwad** Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=(2,5].

a.)Sketch the graph of XA•XB

(which has X with an A subscript and X with B subscript, i suppose means XA composite XB)

b.)Sketch the graph f|A•IB

Now i know how to graph XA and XB but im not sure what to do with a.) and i dont know what b.) is even asking.

Any help or suggestions. Much appreciated.

Try to prove (or note) that in general that, in your notation, . I don't know what they're asking for b) either, what does the vertical line indicate? What are ?

Re: Characteristic Function on A

XAºXB i suppose i should have written it as. XA composite XB. I'm not sure if its the intersection. IB i think is the Identity function: B-->B

Re: Characteristic Function on A

Quote:

Originally Posted by

**Aquameatwad** Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=(2,5].

a.)Sketch the graph of XA•XB

(which has X with an A subscript and X with B subscript, i suppose means XA composite XB)

For any x, . Now, returns either 0 or 1, so what's the value of ?

Quote:

Originally Posted by

**Aquameatwad** b.)Sketch the graph f|A•IB

Quote:

Originally Posted by

**Aquameatwad** IB i think is the Identity function: B-->B

In this case, it looks like , i.e., the composition of the restriction of on and the identity function on . So, . Since is defined on (2, 5], the question now is only to determine for which the function application is defined.

Re: Characteristic Function on A

Well for part a. would (2,5] be on 1? So would it just be as if we were graphing just XB? Cause if i put XB inside XA which is what the composite is wouldnt it just be the intersection of XA and XB?

Its not making sense to my pea brain. (Crying)

Re: Characteristic Function on A

Re: Characteristic Function on A

The syntax and math jargon of this question is probably whats making this difficult to me.

So what does it mean for instance in case1: XA(1) and case 2: XA(0).?

For case 1: Would i graph the line then at y=1, x=[ -1,3) for XA=1. ??

Re: Characteristic Function on A

Before sketching anything, you need to learn to compute compositions of functions. So, what are and , and therefore, what is for all ?

Re: Characteristic Function on A

i understand the composition of functions and relations , but A and B are just sets arent they? This isnt making any sense. The characteristic functions aren't given much explanation in my textbook. So i have no idea what there purpose even is. It's just a review problem our teacher gave us and I'm just trying to graph it.