Composite and Inverse Functions

This investigation leads learners to draw the graphs of y = fg(x) and y = gf(x) for a variety of pairs of functions and to find an algebraic expression of each. The second section looks at pairs of functions which are inverses of each other and are valid for all values of x. The extension material looks at functions and their inverses which raise issues about domain and range of the functions and the need for the function to be one-one.