There is another method we can use to find the inverse of a function. Taking the inverse "reverses" x and f (x) . Thus, in the original function, substitute " x " for " f (x) " and substitute " f -1(x) " for " x ". Then, solve for f -1(x) using inverse operations in the usual manner.
Example 1: f (x) = .
|5x||=||2(f -1(x)) - 1|
|5x + 1||=||2(f -1(x))|
Example 2: f (x) = , x≠1 , f (x) > 0 .
|x(f -1(x) - 1)2||=||1|
|(f -1(x) - 1)2||=|
|f -1(x) - 1||=|
|f -1(x)||=||+ 1|
We can also find the inverse of a function by graphing. The inverse of a
function is a reflection of that function over
y = x
. In other words, all points
(x, y) = (a, b)
(x, y) = (b, a)
coordinates of each point switch:
To find the inverse of a function, reflect the function over the line y = x . Or, find several points on the graph of y = f (x) , switch their x and y coordinates, and graph the resulting points. Connect these points with a line or curve that mirrors the line or curve of the original function.
Example: Find the inverse y = 2x - 1 by graphing: