SOLUTION: State the domain of the following: g(x)=2x+1/x-3

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Question 107683: State the domain of the following:

g(x)=2x+1/x-3

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a "function" must be single-valued+ which means "one and only one"; to each value of x+there is a unique value of y.
The values that x may assume are called the domain of the function, and those are the values for which the function is defined.
In the function +y+=+ax+%2B+b, the domain may include all+real+numbers+; consequently, x could be any+real+number.
But, there is one case in which the domain must be restricted, and that is the case when a denominator may+not+be+0.
So, in this function g%28x%29=%282x%2B1%29%2F%28x-3%29 a denominator x-3 may not be equal to 0 because to divide by 0 doesn’t make a sense.
Let set it equal to 0 in order to find what x may not be in a domain:
x-3+=+0
x+=+0+%2B3
x+=+3
Solution:
In a domain could be all other real numbers except 3.
Domain: (-+infinity, 3] and [3,%2Binfinity)