Question

Determine the domain and range of ( g(x) given ( f(x) = 1/x .

a) Domain (-[infinity], 0) ∪ (0, [infinity]) , Range (-[infinity], -3) ∪ (-3, [infinity])
b) Domain (-[infinity], 0) ∪ (0, [infinity]) , Range (-[infinity], 2) ∪ (2, [infinity])
c) Domain (-[infinity], 0) ∪ (0, [infinity]) , Range (-[infinity], 4) ∪ (4, [infinity])
d) Domain (-[infinity], 0) ∪ (0, [infinity]) , Range (-[infinity], 1) ∪ (1, [infinity])

Answer 1

The domain of g(x) is (-∞, 0) ∪ (0, ∞), and the range of g(x) is (-∞, 0) ∪ (0, ∞).

Step-by-step explanation:

The domain of the function g(x) can be determined by considering the domain of f(x) and understanding how g(x) is related to f(x). Since f(x) = 1/x, the only restriction on the domain of f(x) is that x cannot be equal to 0. Therefore, the domain of g(x) is the same as the domain of f(x) except that it does not include 0. So, the domain of g(x) is (-∞, 0) ∪ (0, ∞).

The range of f(x) = 1/x can be determined by understanding the behavior of the function as x approaches positive infinity and negative infinity. As x approaches positive infinity, f(x) approaches 0, and as x approaches negative infinity, f(x) approaches 0 as well. Therefore, the range of f(x) is (-∞, 0) ∪ (0, ∞).

Since g(x) is defined as f(x), except that it is restricted to the domain of (-∞, 0) ∪ (0, ∞), the range of g(x) is the same as the range of f(x). So, the range of g(x) is (-∞, 0) ∪ (0, ∞).