Question

Find the domain of the given functions: (4 points)

(a) f(x) = 7/x

(b) g(x) = 2x - 1

Answer 1

Domain of f(x) = (-∞, 0) U (0, ∞)

Domain of g(x) = (-∞, ∞)

Explanation:

(a) The domain of f(x) is all real numbers except x = 0, because the denominator cannot be equal to zero. Therefore, the domain of f(x) is:

Domain of f(x) = (-∞, 0) U (0, ∞)

(b) The domain of g(x) is all real numbers, because there are no restrictions on the values of x that can be plugged into the function. Therefore, the domain of g(x) is:

Domain of g(x) = (-∞, ∞)

Answer 2

(a) The domain of f(x) = 7/x is (-∞, 0) U (0, ∞).
(b) The domain of g(x) = 2x - 1 is (-∞, ∞).

Explanation:
a) The function f(x) = 7/x represents a rational function. To find the domain of this function, we need to consider the values that x cannot take, as these would result in an undefined expression. In this case, the expression becomes undefined when the denominator (x) equals zero because division by zero is not defined in mathematics. So, to find the domain, we need to solve the equation x = 0. The solution to this equation is x = 0. Therefore, the function f(x) = 7/x is undefined at x = 0. The domain of the function f(x) = 7/x is all real numbers except for x = 0. In interval notation, we can represent the domain as (-∞, 0) U (0, ∞). (b) The function g(x) = 2x - 1 is a linear function, which means it is defined for all real numbers. In other words, there are no restrictions on the values that x can take. Therefore, the domain of the function g(x) = 2x - 1 is all real numbers. In interval notation, we can represent the domain as (-∞, ∞). In summary: (a) The domain of f(x) = 7/x is (-∞, 0) U (0, ∞). (b) The domain of g(x) = 2x - 1 is (-∞, ∞).