Question

`If:X rarr Y` is a function,then the element of X are called?#

`If:Xrarr Y` is a function,then the element of X are called#

Answer 1

If we have a function `f` such that:

`f: X-> Y`

Then

the set `X` is known as the domain of the function
the set `Y` is known as the range of the function

The domain is the set of input values for which the function is defined.

The range is the set of values which the function produces.

Example 1

`f:X |->Y` defined by `f(x)=sinx` where `X,Y sube RR`

Then:

`X=R` and `Y={x in RR | -1 le x le 1} = [-1,1]`

ie the function can take as input any real number, but the output is restricted to being between `1` and -1#, As verified by the graph of the function
graph{sinx [-10, 10, -5, 5]}

Example 2

`f:X |->Y` defined by `f(x)=sqrt(x)` where `X,Y sube RR`

Then:

`X=Y={x in RR | x ge 0 }`

ie the function can take any nonzero real number as input, and can produce any non-negative number as output. As verified by the graph of the function
graph{sqrtx [-10, 10, -5, 5]}