Answer:
(a) Domain of f(g) : {2, 4, 7, 9|
(b) Range of f(g) : {2, 5}
Step-by-step explanation:
Given the definitions of f and g, you want the domain and range of f(g).
(a) Domain
The composition f∘g means f(g(x)). The values of x for which this composition is defined will be the values of x such that the output g(x) is an input to f(x).
Outputs of g(x) are {2, 4, 7, 8, 9}.
Inputs for which f(x) is defined are {0, 1, 2, 7, 8, 9}. Values on both these lists are {2, 7, 8, 9}.
The domain of g will be the set of input values that gives these output value for g: {2, 4, 7, 9}.
The domain of f(g) is {2, 4, 7, 9}.
(b) Range
The range of f(g) is the set of output values of f(x) that correspond to the inputs f can get from g. Those inputs to f are {2, 7, 8, 9}. The corresponding output values of f are {2, 5, 5, 2}. When listing range values, we only need to list the unique outputs.
The range of f(g) is {2, 5}.
