Finding the domian of function f(x)=x/3x-1

[pulgis]

I know this is the most simple of the problems but I haven't had math in more than a year, so I need some refreshing . Could you please tell me what I need to do to approach this problem? Thank you!

f(x)=x/3x-1

Prisci

 

[o_O]

The domain of a function is basically all the x values that it can have. What value of x CAN'T you have?

 

[pulgis]

it can't be zero... right?

the solution says that it cannot be equal to 1/3... how do i get that?

 

[o_O]

If x = 0, then:

\(\displaystyle f(0) = \frac{0}{3(0) - 1} = \frac{0}{-1} = 0\)

Nothing wrong there.

What I'm trying to get at is when you are dividing, the whole denominator cannot be 0 as it would be an illegal operation. So, what values of x would make the denominator equal to 0?

 

[pulgis]

oh i see! so it cannot be equal to 1/3 becuase the denominator would be 3(1/3)-1 = 3/3 -1 = 1-1 = 0

right?

so i would always look for this right?

 

[o_O]

Yep, basically set the denominator equal to 0 and solve for x:

\(\displaystyle 3x - 1 = 0 \quad \Rightarrow \quad x = \frac{1}{3}\)

And yes, this is the case for any quotients in general. Also, this happens when you try to take square roots or logarithms of negative numbers as you won't get any real solutions so that's something else you should look for.

 

[pulgis]

kool! thank you so much for your help! i think after doing a couple problems everything else will come back to me! thanks again!

 

[stapel]

the solution says that it cannot be equal to 1/3... how do i get that?

You get that by working with the correct function. You posted f(x) as being x/(3x) - 1 = 1/3 - 1 = 2/3, a constant function with only x = 0 being a prohibited value. I'm fairly certain you actually meant the function to be x / (3x - 1), with 3x - 1 = 0, or x = 1/3, being the prohibited value.

Eliz.