Question

Determine the domain of each of the following functions. Enter your answer using interval notation. (a) Domain of ln(28-7x)? (b) Domain of log_9(x²-4)? (c) Domain of ???

Answer 1

The domain of ln(28-7x) is (-∞, 4). The domain of log9(x²-4) is (-2, 2). The domain of ??? cannot be determined without additional information.

Step-by-step explanation:

(a) Domain of ln(28-7x): In order for the natural logarithm function to be defined, the argument (28-7x) must be greater than zero. So, we need to solve the inequality 28-7x > 0. Solving this inequality, we find that x < 4. Therefore, the domain of ln(28-7x) is (-∞, 4).

(b) Domain of log9(x²-4): For the logarithm with base 9 to be defined, the argument (x²-4) must be greater than zero. Solving the inequality x²-4 > 0, we get -2 < x < 2. Thus, the domain of log9(x²-4) is (-2, 2).

(c) Domain of ???: It seems that the question is incomplete, and there is no specific function provided. Therefore, the domain cannot be determined without additional information.

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