# Domain of a Function

• September 30th 2009, 01:59 PM
SHiFT
Domain of a Function
So I know domain implies input, but how would one go about finding the domain of a problem such as this:

$y=\frac{\sqrt{1-x}}{x}$
• September 30th 2009, 02:04 PM
e^(i*pi)
Quote:

Originally Posted by SHiFT
So I know domain implies input, but how would one go about finding the domain of a problem such as this:

$y=\frac{\sqrt{1-x}}{x}$

• The denominator must never equal 0
• Anything under a square root must be greater than or equal to 0

In this case $x \in \mathbb{R} \: , \: x \leq 1 \, , \, x \neq 0$
• September 30th 2009, 02:05 PM
pflo
Quote:

Originally Posted by SHiFT
So I know domain implies input, but how would one go about solving a problem such as this:

$y=\frac{\sqrt{1-x}}{x}$

Two things about functions such as this one: 1) it won't exist when there is a negative inside the square root and 2) it won't exist when you're dividing by zero.

Based on the first thing:
$1-x\ge0$
So $x\le1$

Based on the second thing, the denominator cannot be zero. Since the denominator is x, $x\ne0$

The domain is all real numbers less than or equal to 1 except 0.
• September 30th 2009, 02:14 PM
SHiFT
Thanks a lot guys, It's hard for me to understand a problem when I'm looking at it, but once I see the solution it makes so much sense.
• September 30th 2009, 11:51 PM
A Beautiful Mind
If you get something like this, it's just $x \neq$ anything in the denominator that's going to make it zero.

Since it was just plain old $x$, you'd think about making it zero since any number you could possibly plug in would not make the denominator zero unless it was 0 itself.

This goes for anything like that pretty much.

Like take for instance:

$f(x) = \frac{x+3}{x^2-9}.$

What's gonna make it zero?

Well a negative and a positive squared is always going to end up positive and to make it zero what would you need to get make it that way? Well, you'd need some number $x$squared to make 9. What number $x^2 = 9?$ $3. -3$ also though too because $(-3)^2 = (-3)(-3) = 9.$

$f(x) = \frac{x+3}{9-9}.$

Can't divide by zero.

$x \neq 3$ $or -3.$