example:

Two functions f and g are defined in the figure below. Domain of f Range of f Domain of g Range of g Find the domain and range of the composition g of. Write your answers in set notation. Therefore, the range of g of is (4, 8}. (a) Domain of g of : The function g of can be summarized as follows. (b) Range of g of : EXPLANATION Given functions f and g, we define the composition of g with f, written g of, as follows. ( g of ) ( x ) = 8 (f (x) ) So, to evaluate g of at an input x, we first find f (x). Then, we use f (x) to find g (f (x)). 9 More (a) For the current problem, a sketch of the composition of g with f is shown in the figure below. Range of g Domain of g of Range of g of ANSWER (a) Domain of g of :