Lesson 3: Inverse Function
(1) The meaning of "inverse?
Let f be a mapping from set X to set Y. The inverse of f, denoted by represents the "reverse" mapping from Y back to X.
Let y = f (x), with f (x) = 2x + 1.
f maps x = 3 to y = 7.
Then "reverse" maps y = 7 back to x = 3.
Note: The inverse mapping can be obtained by expressing x
in terms of y, i.e.
(2) Existence of inverse function
If a function f is 1 to 1, then it will have an inverse function, i.e. f must satisfy the horizontal line test.
(3) Domain, Rule & Range
To find the rule of , let y = f (x) and rearrange x in terms of y. If there are multiple expressions for x, only select the one which satisfies .
Let the function f be defined as follows:
(4) Graph of inverse functions
The graph of a function and its inverse are reflections of each other about the line y = x. Essentially, all the original x and y coordinates will be interchanged.
Note: If the graph of a function f and its inverse intersect along the line y = x, we can obtain the point of intersection by solving f (x) = x.