SOLUTION: What is the domain of f in interval notation if f(x) = ( x – 5 )^1/2? Thanks.    

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Question 1060082: What is the domain of f in interval notation if f(x) = ( x – 5 )^1/2?
Thanks.
   
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
( x – 5 )^1/2 is the same as sqrt(x-5)

sqrt is shorthand for "square root"

With square roots, we cannot have the stuff inside be negative

x-5 cannot be negative. So force it to be either 0 or a positive value. I.e,

x-5+%3E=+0

isolate x and we get

x+%3E=+5

Which is the domain. It's the set of allowed x values we can plug in. We can plug in 5 for x or any number that is larger than 5.

The domain in set builder notation would look like this


In interval notation, the domain is written like this [5, \infty)