What is the domain and range of # y=sqrt( x-4)#?

1 Answer
Apr 16, 2017

Answer:

Domain: #x>=4#
Range: #y>=0#

Explanation:

Any number inside a square root has to be positive or #0# or else, the answer will be a complex solution. With that being said, #x-4# has to be greater than or equal to #0#:

#x-4>=0#

Solve this equation to find the domain. Add #4# to both sides:

#x>=4#

So our domain is that x has to be greater than or equal to #4#.

Since the square root can never yield a negative number, #y# will always be positive or #0#. So the range of #y# is that:

#y>=0#