SOLUTION: Find the domain and range of the INVERSE of the given function. Square root x-3 I think the answer is Domain [0,infenity), Range [3,0) or the answer might be Domain: all real num

Question 242808: Find the domain and range of the INVERSE of the given function.
Square root x-3
I think the answer is Domain [0,infenity), Range [3,0) or the answer might be Domain: all real numbers; range [3,infenity).
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Given that , 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 or

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

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 or [0, inf),
and Range is or [3, inf).

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