# Math Help - Question...

1. ## Question...

okay... $f(x) = |x|/x$

anyway I am trying to find the domain and range which I am expressing in interval notation...

I am getting:
Domain: (-infinity, 0) (0, infinity)
Range: y is equal to 1 or -1 thats it... how would I express that in interval notation?

2. Hello,
Originally Posted by CalcGeek31
okay... $f(x) = |x|/x$

anyway I am trying to find the domain and range which I am expressing in interval notation...

I am getting:
Domain: (-infinity, 0) (0, infinity)
Range: y is equal to 1 or -1 thats it... how would I express that in interval notation?
\begin{aligned} f ~:~ & ]-\infty, ~0[~ \cup ~ ]0, ~+\infty[ & \mapsto & \quad \{-1~,~1\} \\
& \quad \quad \quad \quad x & \mapsto & \quad y \end{aligned}

It can also been written :

\begin{aligned} f ~:~ & \mathbb{R}\backslash \{0\} & \mapsto & \quad \{-1~,~1\} \\
& \quad x & \mapsto & \quad y \end{aligned}

{ } usually defines a set of elements.

3. I completely understand that... but [-1, 1] means also all numbers in between but that is not true... it can only equal 1 or -1...

4. Originally Posted by CalcGeek31
I completely understand that... but [-1, 1] means also all numbers in between but that is not true... it can only equal 1 or -1...
I wrote {-1,1}, not [-1,1]

Look carefully ^^

5. Ohh... what if Im only using () and [] would it be [-1, -1] [1, 1]?

6. Originally Posted by CalcGeek31
Ohh... what if Im only using () and [] would it be [-1, -1] U [1, 1]?
I guess it would work, but I've never seen this notation

Or you can write $y=f(x)=\left\{\begin{array}{c} -1 \\ 1 \end{array} \right.$ but it wouldn't really fit in here.

7. according to what Ive learned... () is used when the number is not equal to this end... and [] is used when it is equal to either end... EX 2 < x <= 5 would be (2, 5]

8. Originally Posted by CalcGeek31
according to what Ive learned... () is used when the number is not equal to this end... and [] is used when it is equal to either end... EX 2 < x <= 5 would be (2, 5]
I know it, but what I meant is that I've never seen anyone (I'm not saying everybody) using these notations to talk about only one element. We rather use { }

9. Originally Posted by Moo
I guess it would work, but I've never seen this notation

Or you can write $y=f(x)=\left\{\begin{array}{c} -1 \\ 1 \end{array} \right.$ but it wouldn't really fit in here.
That is set interval notation. You can just write: -1 U 1, but you can still use a set to represent the range: {-1, 1}

10. just wondering and thank you by the way... would you happen to help me with my other question?(Question #2...)