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.

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:

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.