SOLUTION: Please help me solve this equation {{{f(x)=(x^2-x-12)/(x-2)}}} Find: (x+3)(x-4)/x-2 (a)domain: +3 or -4 (b)zeros,if any: All real numbers except 0 and -2 Is this correct?

Algebra ->  Functions -> SOLUTION: Please help me solve this equation {{{f(x)=(x^2-x-12)/(x-2)}}} Find: (x+3)(x-4)/x-2 (a)domain: +3 or -4 (b)zeros,if any: All real numbers except 0 and -2 Is this correct?      Log On


   

Question 22362: Please help me solve this equation f%28x%29=%28x%5E2-x-12%29%2F%28x-2%29
Find: (x+3)(x-4)/x-2
(a)domain: +3 or -4
(b)zeros,if any: All real numbers except 0 and -2
Is this correct?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
not quite sure what you are asking here. I think you are asking for your answers to be checked?

f(x) is re-written as %28%28x%2B3%29%28x-4%29%29%2F%28x-2%29, correct.

So, domain. This is ONLY asking you, what values of x can you put in to this equation? To answer this, it is easier to ask yourself, which x-values can i NOT put into the equation? That answer is x=+2, since this value, makes the denominator zero and then the function goes haywire there!.
So, the domain is ANY VALUE OF x, but not +2.
This is written as xeR, x /= +2 (i cannot write the correct symbols here: /= is supposed to be an equals with a diagonal line through it)

Zeroes? These are the roots of the equation. where does it cross the x-axis. The answer is at points x=-3 and x=4.

The graph is:
graph%28200%2C200%2C-5%2C5%2C-10%2C10%2C+%28%28x%2B3%29%28x-4%29%29%2F%28x-2%29%29

but note that the vertical line at x=2 is NOT part of the graph. The graph is 2 separate curves that head towards but never quite reach the x=2 vertical...this is called the asymptote.

Hope this helps

jon.