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Home : Math & Science : Math Study Guides : Algebra II : Operations with Functions : Other Methods of Finding Inverses
Other Methods of Finding Inverses
Finding the Inverse of a Function by Isolating f-1(x)
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) = .
Example 2: f (x) = , x≠1, f (x) > 0.
Domain of f-1: x > 0. Range of f-1: f-1(x)≠1.
Finding the Inverse of a Function by Graphing
We can also find the inverse of a function by graphing. The inverse of a
function is a reflection of that function over
the line y = x. In other words, all points (x, y) = (a, b) become (x, y) = (b, a). The x and y coordinates of each point switch:
Inverse of a Graph
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:
Inverse of y = 2x - 1
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