SOLUTION: Find the domain of the following function: {{{y=(3x-2)/(4x+1)}}} Would I go about this by solving for x? I'm not really sure how to start this. If you could just show me

Algebra ->  Algebra  -> Functions -> SOLUTION: Find the domain of the following function: {{{y=(3x-2)/(4x+1)}}} Would I go about this by solving for x? I'm not really sure how to start this. If you could just show me       Log On

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Question 92801: Find the domain of the following function:
y=%283x-2%29%2F%284x%2B1%29

Would I go about this by solving for x? I'm not really sure how to start this. If you could just show me the steps to finding the solution for this problem, I would greatly appreciate it!!!
Answer by bucky(2097) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
y=%283x-2%29%2F%284x%2B1%29
.
The domain is the spectrum of values that x can take. In this problem there is only one
consideration that limits the value of x. Notice that there is a denominator that contains x.
Also recall that algebraic rules do not permit division by zero. Therefore, the denominator
cannot equal zero.
.
So we can write the equation:
.
4x+%2B+1+=+0
.
Subtract 1 from both sides and we get:
.
4x+=+-1
.
Finally, divide both sides by 4 to find x and you get:
.
x+=+%28-1%29%2F4
.
This tells us that if x+=+%28-1%29%2F4 then the denominator equals zero. Therefore,
x cannot be equal to %28-1%29%2F4. Other than that single exception, x can have any value
from minus infinity to plus infinity.
.
Hope this helps you to understand the problem a little more.