Two functions g and f are defined in the figure below Find t

Two functions g and f are defined in the figure below. Find the domain and range of the composition f degree g. Write your answers in set notation. Domain of f degree g : Range of f degree g :

Solution

The composition f o g has domain = range of function g - {1} [ We subtracted 1 because 1 is not in domain of f and hence f(1) is not defined.]

= { 3, 7, 8, 9}

The composition f o g has range = range of f - {2} [ we subtracted 2 because it will only be there when we have 5 as input variable for f but 5 can never be the output variable of g ]

= {1 , 9 }