IGCSE MATH Topic : Functions – Domain, Range, Inverse

Briefly given a function f(x), the domain is the set of valuesxmay 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 R, 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 is R orand 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.