In this problem, we assume that is a whole number. The definition of inverse functions tells us that a function
has an inverse function if and only if the function is one-to-one, that is, if there is no any horizontal line intersecting the graph of
at more than one point. This only happens if
is odd. This is called the Horizontal Line Test for Inverse Functions. So let's take two examples:
FIRST:
Since n is even, an horizontal line will pass through two points as indicated in the first figure below.
SECOND:
Since n is odd, an horizontal line will pass through just one point as indicated in the second figure below.
Let's first take a look at function G. From the first to second row, the x-value increases by 2, and the y-value increases by 8.
Thus, function G has a rate of change of , or 4.
In function H, there is a "2" before the "x", which means function H has a rate of change of 2.
Thus, the statement that is true is:
Let me know if you need any clarifications, thanks!
~ Padoru