Question

Let h:{0,1,7} → Z, where Z is the set of Integers, be defined by h(x) = x^2 + 10. Determine the domain, codomain, and range of h.

Answer 1

The domain of the function h(x) = x^2 + 10 is {0, 1, 7}, the codomain is the set of all integers Z, and the range is the set of outputs {10, 11, 59}.

Step-by-step explanation:

The function h is defined as h(x) = x^2 + 10, where the domain is explicitly provided as the set {0, 1, 7}. We need to determine the domain, codomain, and range of this function.

• The domain of a function is the set of all possible inputs. In this case, the domain of h is given by {0, 1, 7}.
• The codomain is the set where the function's outputs can lie, which is given as Z, the set of all integers.
• The range is the set of all actual outputs from the function. We calculate the outputs by applying the function to each element of the domain:

1. h(0) = 0^2 + 10 = 10
2. h(1) = 1^2 + 10 = 11
3. h(7) = 7^2 + 10 = 59

Therefore, the range of h is the set {10, 11, 59}.