Thread: 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.

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 ?

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

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 ?

Originally Posted by Aquameatwad

b.)Sketch the graph f|A•IB

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.

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.

Originally Posted by emakarov

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

If I understand the definitions correctly,





Case 1: . Then , so

Case 2: . Then , so

As an aside note, one of the confusing things about is the different meaning given to real numbers. The output of is 0 or 1, yet it is interpreted as any other real number and is fed to . In programming, it would be clearer to make and return Boolean values True and False instead of numbers 1 and 0. Then would be ill-typed.

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. ??

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

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.