Find the domain of the function. (Enter your answer using interval notation.)f(x) = log9(12 − 4x)
Question
Find the domain of the function. (Enter your answer using interval notation.)
f(x) = log_9(12 - 4x)
Solution
The domain of a logarithmic function is the set of all possible input values (x-values) that will output real numbers. For the function f(x) = log9(12 - 4x), the argument of the logarithm (12 - 4x) must be greater than zero.
Here are the steps to find the domain:
- Set the argument of the logarithm greater than zero.
12 - 4x > 0
- Solve the inequality for x.
-4x > -12
x < 3
So, the domain of the function f(x) = log9(12 - 4x) is x < 3. In interval notation, this is (-∞, 3).
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