SOLUTION: State the domain of the rational expression in the set builder notation. 6x^2-11x+3/4x^2-12x+9

Question 138367: State the domain of the rational expression in the set builder notation.
6x^2-11x+3/4x^2-12x+9
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The domain of a function is the set of all values of the independent variable, x in your case, for which the function is defined. What you need to do is find those values for which the function is undefined and define the set that excludes those values.

Each of the numerator and denominator polynomials are individually defined for all real numbers, so your only concern with the given rational expression is finding those values of x that would make the denominator equal zero.

Take the denominator polynomial, set it equal to zero, and solve the resulting quadratic. The value or values you obtain as roots are the values you must exclude from the set of real numbers when you describe the domain of the rational function. Hint: The denominator polynomial is a perfect square.

Set builder notation will look something like this, if you say is your domain. ={ | }, read "The domain of f is the set of all real numbers x such that x is not equal to a" Of course, you must substitute the appropriate value for a that you discovered when you solved the denominator quadratic.
RELATED QUESTIONS
State the domain of the given rational expression in set-builder notation. 8x(2) + 1... (answered by ewatrrr,jsmallt9)

given:f(x)=x^2-6x/2x^2-11x-6 A. factor the numerator and the denominator B. write... (answered by Fombitz)

given:f(x)=(x^2-6x)/(2x^2-11x-6) A. factor the numerator and the denominator B.... (answered by Fombitz)

Find the domain of the function express in set builder notation. f(x)=... (answered by stanbon)

Graph the relation defined by the equation x^2+(y-3)^2 = 16 . Express the domain and the... (answered by lwsshak3)

Determine the solution set to the inequality. Express your answer in set builder... (answered by kmcruz09)

Solve the following inequality and write your solution using set builder notation... (answered by swincher4391)

Find the domain written in set-builder notation:... (answered by richard1234)