Video Transcript
Find the common domain between the
functions 𝑛 sub one of 𝑥 equals seven over eight 𝑥 and 𝑛 sub two of 𝑥 equals
nine over 𝑥 minus two.
First, we recall the common domain
between any two functions is the intersection of their domains. In this case, we must find the
domains of 𝑛 sub one of 𝑥 and 𝑛 sub two of 𝑥. Then we can find their
intersection. So next, we remind ourselves of how
to find the domain of a rational function. The domain of a rational function
is the set of real numbers, but we exclude any values of 𝑥 that make the
denominator equal zero. So, let’s take the function 𝑛 sub
one of 𝑥. Its domain is going to be the set
of real numbers, but we need to exclude values of 𝑥 that make the denominator eight
𝑥 equal to zero. To solve for 𝑥, we divide both
sides of the equation by eight and we find the value of 𝑥 that satisfies this
equation is zero. So, the domain of 𝑛 sub one of 𝑥
is the set of real numbers minus the set containing zero.
Now let’s consider the function 𝑛
sub two of 𝑥. This time we need to exclude values
of 𝑥 that make the denominator 𝑥 minus two equals zero. The value of 𝑥 that satisfies this
equation is two. And so the domain of 𝑛 sub two is
the set of real numbers minus the set containing two. The common domain, then, is the
intersection of the two domains we have just found. So, we are going to have to take
the set of real numbers and exclude both zero and two. Hence, the common domain between
the two functions we were given is the set of real numbers minus the set containing
zero and two.
