state the domain of the following function in interval notation
h(x)=sqrt 3x+2
explain how this is the answer
The domain of the function h(x) = √(3x+2) consists of all values of x for which the expression under the square root is non-negative, since the square root of a negative number is not defined in the real number system.
To find the domain, we need to solve the inequality 3x+2 ≥ 0:
3x + 2 ≥ 0
3x ≥ -2
x ≥ -2/3
Therefore, the domain of the function h(x) is all real numbers greater than or equal to -2/3.
In interval notation, this can be represented as: [-2/3, ∞). This indicates that x can be any value greater than or equal to -2/3.