Question

Given A = {-3, -2, 3, 2} and f = {x, 1/x²},

a) List the domain of f
b) Is f a function?

A. Domain: {-3, -2, 2, 3}; Yes
B. Domain: {-3, -2, 2, 3}; No
C. Domain: All real numbers; Yes
D. Domain: All real numbers; No

Answer 1

The domain of f is {-3, -2, 2, 3}; Yes, f is a function.

Step-by-step explanation:

a) The domain of a function is the set of all possible input values. In this case, the domain of f is the set of numbers that can be substituted for x in the function f = {x, 1/x²}. Since x cannot be equal to 0 (because that would result in division by zero), the domain of f is the set of all real numbers except 0. Therefore, the domain of f is {-3, -2, 2, 3}.

b) To determine if f is a function, we need to check if each input value in the domain produces only one output value. In the given function f = {x, 1/x²}, each input value x corresponds to a unique output value, so f is indeed a function.

Therefore, the correct answer is A. Domain: {-3, -2, 2, 3}; Yes.