Find the domain:
h(x)=√(x+4)
How do I work this problem?
√u is defined only for u>=0
so, √(x+4) is defined only for (x+4) >= 0, or
x >= -4
the domain is thus all reals x >= -4
To find the domain of a function, you need to determine the set of all possible input values that the function can accept. In this case, we have the function h(x) = √(x + 4).
For the square root function, the value inside the square root (i.e., the radicand) must be non-negative because the square root of a negative number is not defined in the real number system.
To find the domain of h(x), we set the radicand x + 4 ≥ 0 and solve for x:
x + 4 ≥ 0
x ≥ -4
From this inequality, we can deduce that x must be greater than or equal to -4 for the function h(x) to be defined. Therefore, the domain of h(x) is all real numbers greater than or equal to -4, or in interval notation:
Domain: [-4, ∞)