What is the domain and range of #g(x) = sqrt(x-2)#?

1 Answer
Jacobi J.
Mar 10, 2018

Domain: #x\>=2#
Range: #y>=0#

Explanation:

If we're concerned with real solutions, #sqrt(x-2)# cannot take on any values less than zero. We can model this with the following inequality to figure out the domain:

#sqrt(x-2)\>=0#

Squaring and adding #2# to both sides, we get:

#x\>=2#

(This is our domain)

What else do we know about square roots? Above, we said we cannot have any values less than zero. This is our range.

Given a domain of #x>=2#, the range will be #y>=0#, because the lowest value we can plug in, #2#, will evaluate to #0#.

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