Using interval notation, identify the domain for the function: f(x)=sqrt of x-9

Question

how to work this problem?

Answer 1

Since the number under the square-root cannot be negative, we set this inequality to find the domain.

 

x - 9 ≥ 0

 

 

Solve the inequality for x.

 

x ≥ 9

 

 

The domain in interval notation is  [9, ∞).

 

 

Note: When finding the domain of a function that has an even root, the argument that is inside that root must greater than or equal to zero.  This is because any number raised to an even power is always positive, and zero raised to any power is always zero.

Answer 2

[9,∞) because x can be 9 or greater but x cannot be less than 9 because that means you would have a negative number under the square root sign giving you an imaginary number