The first 5 outputs are:
As you can see, the outputs keep doubling each time we increment x by 1.
This can be written formally, observing that if you know the value of , the next value will be
So, again, we've shown that the next value is twice the previous one, so you have
Answer:
<u>Question 1</u>
The function is one-to-one, so it does have an inverse.
The inverse of +6 is -6, so
Therefore, g(x) is the inverse of f(x).
<u>Question 2</u>
The function is one-to-one, so it does have an inverse.
To find the inverse, replace f(x) with y:
Rearrange the equation to make x the subject:
Replace x with and y with x:
Therefore, g(x) is the inverse of f(x).