Video Transcript
Given that 𝑓 of 𝑥 is equal to
three to the power of 𝑥 minus eight, find 𝑓 of 𝑥 plus nine.
In this question, we are told that
the function 𝑓 of 𝑥 is equal to three to the power of 𝑥 minus eight. And we are asked to find an
expression for the function 𝑓 of 𝑥 plus nine. In order to do this, we will
substitute 𝑥 plus nine for 𝑥 in our original function. We have three to the power of 𝑥
plus nine minus eight. We can remove the parentheses and
then collect like terms. Since nine minus eight is equal to
one, our expression simplifies to three to the power of 𝑥 plus one. And we can therefore conclude that
if 𝑓 of 𝑥 is equal to three to the power of 𝑥 minus eight, then 𝑓 of 𝑥 plus
nine is equal to three to the power of 𝑥 plus one.
