SOLUTION: Find the domain and range of the following function in interval form. {{{ sqrt( x^2+3x-4 ) }}} divided by {{{ sqrt( (x-2)^2 ) }}}

Question 1003177: Find the domain and range of the following function in interval form.
divided by
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

The restrictions to the domain are
denominators cannot be zero, so <--> , and
expressions inside square roots cannot be negative, so .
(We know that is not negative).
is negative for ,
so ((-4,1) is not part of the domain,
and we knew that is not part of the domain, either.
For any other value of , is defined, so
the domain of is

.

The function cannot be negative, because square roots are non-negative in their domain.
We know for .
===

Since is continuous in ,
, and

,
takes all values from to in .
The range of in the interval is

.
Whatever it does in the rest of its domain, it cannot be negative,
so the range of across all of its domain is

.
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