Question 242808
Given that {{{f(x)=sqrt(x-3) }}}, there is a restriction on the values of x (Domain!), because of the square root operation.  Whatever is INSIDE the square root (this is called the RADICAND!), must be greater than or equal to zero.


So, Domain is {{{x-3>=0}}} or {{{x>=3}}}


Now, the Range is the set of all resulting y values. Because y = a square root, y cannot be negative.  Also, the values of y increase without bound, so the 
Range is {{{y>=0}}}


What we just determined was the DOMAIN and RANGE of the FUNCTION.  Now, for the INVERSE FUNCTION, DOMAIN and RANGE are REVERSED!


For the INVERSE FUNCTION, Domain is {{{x>=0}}} or [0, inf),
and Range is {{{y>=3}}} or [3, inf).


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus