How do you find the domain and range of #f(x)=x#?

1 Answer
Aug 14, 2017

Answer:

The domain of #f(x) = x# is the whole of the real numbers #RR#. The range is also the whole of #RR#.

Explanation:

Given:

#f(x) = x#

  • The domain of #f(x)# is the set of values for which #f(x)# is defined. In the context of Algebra I that means a subset of the real numbers #RR#. In the case of the given #f(x)#, it is well defined for any #x in RR#, so the domain is the whole of #RR#, i.e. #(-oo, oo)#

  • The range of #f(x)# is the set of values that it can take for some value of #x#. Given any real number #y#, let #x = y#. Then #f(x) = x = y#. So the range of #f(x)# is the whole of #RR# too.

The graph of #f(x) = x# is a diagonal line like this:

# graph{x [-10, 10, -5, 5]}

For every #x# coordinate there is a corresponding point on the line. That tells us that the domain of #f(x)# is the whole of #RR#.

For every #y# coordinate there is a corresponding point on the line. That tells us that the range of #f(x)# is the whole of #RR#.