Question

Find the domain of y = log(2 - 12). The domain is:

a. ∅ (empty set)
b. ℝ (all real numbers)
c. (−[infinity], 2)
d. (−[infinity], 2] ∪ (2, [infinity])

Answer 1

The domain of the logarithmic function y = log(2 - 12) is the empty set (∅).

Step-by-step explanation:

The domain of a logarithmic function is determined by the restrictions on the input values that produce a valid output. In this case, we have the function y = log(2 - 12). The logarithm function is only defined for positive values, so the argument inside the logarithm should be greater than zero.

Solving the inequality 2 - 12 > 0, we find that 2 > 12. However, this is not possible. Therefore, there are no values of x that make the expression 2 - 12 positive. As a result, the domain of y = log(2 - 12) is the empty set (∅).