Video Transcript
If 𝑔 such that the domain nine,
10, 11, 12, 13 produces a range of positive integers, where 𝑔 of 𝑥 equals 17𝑥
minus 18 and 𝑔 of 𝑘 equals 203, find the value of 𝑘.
The function we’re working with is
𝑔 of 𝑥 equals 17𝑥 minus 18. And we also know that we’re dealing
with a limited domain of nine, 10, 11, 12, and 13. We’ve been told 𝑔 of some 𝑘-value
is equal to 203. If we take this 203 and set the
17𝑥 minus 18 equal to that value and then solve for 𝑥, we’ll be finding our
missing 𝑘-value.
And that means our first step will
be solving for 𝑥 here. To do that, we add 18 to both sides
of the equation, which gives us 221 equals 17𝑥. From there, we divide both sides of
the equation by 17, which tells us that 13 is equal to 𝑥. We’re saying that 𝑔 of 13 equals
203. Before we go on though, it’s good
to check and make sure that a domain of 13 is possible. Since 13 is included in the set of
domains, that is possible. And we can say if 𝑔 of 𝑘 equals
203, then 𝑘 must be equal to 13.
