How do you find the domain of #y=(2x)/(x+9)#?

1 Answer
Oct 3, 2016

Answer:

#x!=-9# or interval notation #(-oo,-9) U (-9,oo)#

Explanation:

If a value of #x# results in #y# being "undefined", that value of #x# is not included in the domain. The domain is the allowed values of #x#.

For a rational equation like this example, dividing by zero will result in an undefined #y#. So, the denominator should not equal zero.

#x+9!=color(white)a0#
#color(white)(a)-9color(white)(aa)-9#

#x!=-9#

A value of #-9# will result in a zero in the denominator, so #-9# is not be included in the domain.

In interval notation, this is written as #(-oo,-9)U(-9,oo)#