Why cant I do this? (Regarding finding domain of function)

[nukeman]

Homework Statement

Problem:

http://archives.math.utk.edu/visual.calculus/0/domain.1/f6.gif

Homework Equations

The Attempt at a Solution

Look at the pic, and tell me again why I can't do this:

http://i47.tinypic.com/bhadsj.jpg

 

[aftershock]

-4x +4 is not x

Also be careful with the direction your inequality sign is supposed to point if you start dividing by negatives.

 

[Mark44]

In addition to what aftershock said, you are missing something else. For f(x) to be defined, it must be true that 9 - 4x ≥ 0 AND 2x - 1 > 0. The domain for this function will be all of the numbers that satisfy both inequalities.

Also, you have a mistake in this work, similar to the one that aftershock pointed out.
2x - 1 > 0
2x > 1 (OK, so far)
Then you subtract 2 from both sides. What's wrong with that is that 2x - 2 ≠ x. To isolate x, divide both sides by 2.