Ive been shown that a function can be written like so
f:X->Y,f(x)=rule
where X is the Domain and Y, the co-domain. Firstly, what is the co-domain? Ive tried looking it up but all I get is "the set of which y values fall in".
If that is the case, say for the function, y=1/(x-1), do I write it like this
f:R\{1}->R\{0},f(x)=1/(x-1)
or instead of R\{0}, just
f:R\{1}->R,f(x)=1/(x-1)?? Where R is the set of all real numbers.
And please, if the answer is both, which would be "more right"?
i don't really know because one where is your numbers at
The co-domain of a function refers to the set of all possible outputs or values that the function can take. It is often denoted by the symbol Y. In other words, it is the set of y-values that can be produced when we apply the function to the input values in the domain.
For the function f(x) = 1/(x-1), the domain would be all real numbers except x=1. Therefore, you would write it as:
f: R\{1} -> R\{0}, f(x) = 1/(x-1)
Here, R\{1} represents the set of all real numbers excluding 1, and R\{0} represents the set of all real numbers excluding 0.
While both representations are correct, the first one (f: R\{1} -> R\{0}, f(x) = 1/(x-1)) is more specific and accurately reflects that the co-domain excludes the value 0. It provides additional information about the function and the set of possible output values. However, if the context allows for it and excluding 0 from the co-domain is not important, you can simply write:
f: R\{1} -> R, f(x) = 1/(x-1)
In summary, both representations are valid, but the more specific one (excluding 0) provides clearer information about the function and the possible output values.