Question 202608
{{{f(x)=log(2, (6-x))}}}
The domain of a function, if not explicitly stated, is all Real numbers except those that would result in something you cannot allow to occur:<ul><li>zeros in denominators</li><li>negative numbers in the radicands of even-numbered roots</li><li>Zero or negative arguments to log functions</li><li>Other "no-no's" like {{{tan(pi/2)}}}, etc.</li></ul>
The only thing you need to avoid for f(x) is a zero or negative argument to the log function. Worded positively, we only want to allow x-values that make the argument to the log positive. In other words:
(6-x) > 0
The simplest way to solve this is to add x to both sides:
6 > x
This is our domain. The tricky part is to read this correctly. This says "x is less than 6". (<b>Always</b> read inequalities from where the variable is. Since this inequality has the variable on the right we start reading from the right and read right-to-left! Read this way it says "x is less than 6".)