Probably The Last One: Advanced Math Help?

Question

Find the domain of the function f (x) ={square root of} (2x+5 / 3x-2)

Read as thus: f of x equals the square root of [2x+5 divided by 3x minus 2].

Please give as much detail as possible, not just an answer!

Thanx a bunch!

For a bonus...

What does the "U" in 'x < -5/2 U x > 2/3' mean or stand for? If you would tell me this I would be in your debt a lot!

Thanx a bunch!

Answer 1

so which one?
1♥ f(x)=√(2x+5/(3x) –2);
2♥ f(x)=√((2x+5)/(3x) –2);
3♥ f(x)=√(2x+5/(3x –2));
4♥ f(x)=√((2x+5)/(3x –2));
5♥ f(x)= √(none of them);

can't wait, i quit; click me if in need

Answer 2

The expression under the radical must be >0, so ((2x+5)/(3x-2)) > 0. This will happen when:

1) both 2x+5 > 0 and 3x - 2 > 0, or x > -5/2 and x > 2/3 --> x > 2/3

2) both 2x+5 < 0 and 3x-2 < 0, or x < -5/2 and x < 2/3 --> x < -5/2.

So the domain is x < -5/2 U x > 2/3.

Of course, 3x-2 <> 0, but since the solution does not include x = 2/3 you don't have to worry about a zero in the denominator.

edit:
The "U" stands for "union", meaning that I was taking the union of the two sets of real numbers x < -5/2 and x > 2/3.

Answer 3

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