# Thread: Zeroes of a function

1. ## Zeroes of a function

Okay. I got this function.

$f(x)= x/9x^2-4$

The answer is zero, but I don't understand how it's zero because I worked it out like this.

I took the bottom half and realized it was $(3x+2)(3x-2)$.

$3x+2=0$
$3x=-2$
$x= -2/3$

$3x-2=0$
$3x=2$
$x = 2/3$

So what does that mean?

$2/3$

----
$
9 (2/3)^2-4$

The bottom half would be zero after the computation, am I right? And you can't divide by zero. But how does that make x zero?

2. Originally Posted by A Beautiful Mind
Okay. I got this function.

$f(x)= x/9x^2-4$

The answer is zero, but I don't understand how it's zero because I worked it out like this.

I took the bottom half and realized it was $(3x+2)(3x-2)$.

$3x+2=0$
$3x=-2$
$x= -2/3$

$3x-2=0$
$3x=2$
$x = 2/3$

So what does that mean?

$2/3$

----
$
9 (2/3)^2-4$

The bottom half would be zero after the computation, am I right? And you can't divide by zero. But how does that make x zero?
Could you state the problem please? Are you looking for the domain of the function, or trying to find the zeros? If you are trying to find the zeros, there is only one.

Is the problem written like this $\frac{x}{9x^2-4}$ ?

3. Originally Posted by A Beautiful Mind
Okay. I got this function.

$f(x)= x/9x^2-4$

The answer is zero, but I don't understand how it's zero because I worked it out like this.

I took the bottom half and realized it was $(3x+2)(3x-2)$.

$3x+2=0$
$3x=-2$
$x= -2/3$

$3x-2=0$
$3x=2$
$x = 2/3$

So what does that mean?

$2/3$

----
$
9 (2/3)^2-4$

The bottom half would be zero after the computation, am I right? And you can't divide by zero. But how does that make x zero?
You just found the two vertical asymptotes.

$x=\frac{2}{3}$ and $x=-\frac{2}{3}$

4. Originally Posted by VonNemo19
Could you state the problem please? Are you looking for the domain of the function, or trying to find the zeros? If you are trying to find the zeros, there is only one.

Is the problem written like this $\frac{x}{9x^2-4}$ ?
I did state the problem and yes, the problem is written like that.

I have another function I'm not sure about.

This time it's
$\frac{x^2-9x+14}{4x}$

OK, Factor the top one and I get x = 7 and x = 2.

What I'm suppose to be doing is finding the zeroes of the function algebraically.

5. Originally Posted by VonNemo19
Could you state the problem please? Are you looking for the domain of the function, or trying to find the zeros? If you are trying to find the zeros, there is only one.

Is the problem written like this $\frac{x}{9x^2-4}$ ?
Originally Posted by A Beautiful Mind
I did state the problem and yes, the problem is written like that.
VonNemo asked if you're trying to find the zero(s) of the function? Where does the graph cross the x-axis? If that is the case, solve this:

$\frac{x}{9x^2-4}=0$