Find the domain of the function. (Enter your answer using interval notation.) f(

Algebra
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Find the domain of the function. (Enter your answer using interval notation.)
f(x) = log6(9 − 3x
Jul 17th, 2015

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The argument of a logaritmic function must be greater than zero. So we would have:

f(x) = log6(9 - 3x)   ----------->  9 - 3x > 0 . So now we solve this linear inequality for x like this.

9 - 3x > 0  --------->  9 - 3x + 3x > 0 + 3x  ----------> 9 > 3x  --------> 9/3 > 3x/3  ---------> 3 > x -------> x < 3

So the solution would be the numbers less than 3, in other words, it would be from - infinity to 3 opened (it doesn't include the endpoint). So finally, our final answer in interval notation is:

(-infinity, 3)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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