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