SOLUTION: Find the domain of f(x)=sqrt x-4. thanks

Question 202032: Find the domain of f(x)=sqrt x-4. thanks

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Remember you cannot take the square root of a negative value. So that means the argument must be greater than or equal to zero (i.e. the argument must be non-negative)

Set the inner expression greater than or equal to zero

Add 4 to both sides

Combine like terms on the right side

So that means x must be greater than or equal to in order for x to be in the domain

So the domain in set-builder notation is

So here is the domain in interval notation: [4,

)

Notice if we graph , we get
notice how the graph never crosses the line . So this graphically verifies our answer.

and we can see that x must be greater than or equal to in order to lie on the graph

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