Find the domain of the function 𝑓 of 𝑥 is equal to the square root of 𝑥 minus 27.
Remember, the domain of a function is the set of all possible values that we can put into that function so that we yield a real output. More formally, the domain of a function 𝑓 of 𝑥 is a set of possible values of 𝑥 such that the expression 𝑓 of 𝑥 is defined. So let’s identify our function. It’s given by 𝑓 of 𝑥 is equal to the square root of 𝑥 minus 27.
Now, obviously, negative 27 is independent of 𝑥. So we might begin by asking ourselves, “Well, what’s the domain of the function the square root of 𝑥?” Well, the square root function is defined when 𝑥 is nonnegative, in other words for all 𝑥-values greater than or equal to zero. And so we can say that any values of 𝑥 that we substitute into the function the square root of 𝑥 minus 27 that are greater than or equal to zero will yield real outputs. And so the domain is indeed the set of numbers greater than or equal to zero, in other words the left-closed, right-open interval from zero to ∞.