The use of the vertical line test determines if a line equation is a function.

If the vertical line intersects only 1 point, the line equation is a function. If the vertical line intersects more than 1 point, the line equation is not a function.

The functions f and g are defined as follows:

Where λ is a constant.

(i) Given that gf exists, find the largest value of λ.

In the rest of the questions, use the value of λ found in part (i).

(ii) On the same diagram, sketch the graph of , and , showing clearly the relationship between the graphs.

(iii) Hence find the exact solution of