Domain, Range and Inverse
Briefly given a function f(x), the domain is the set of values x may have. If we have the graph of f(x) we may be able to read the domain off the x – axis. The graph below is y=ln(x). The domain is obviously, from the x – axis, x>0. It is much harder to see that the range, the set of values y may have, is the set of real numbers, also writtenor The endpoints are not included.
The graph above isUnless we restrict the domain in some way, for example,, then the domain isand the range we can read off the y axis: [-3,3]. The square brackets indicate the endpoints are included in the range.
To find the graph of the inverse of a function we reflect the graph of the function in the line
This is shown above. The red curve is the curveThe inverse tois the curveshown in blue.