SOLUTION: The function g is defined below. g(x)=(x-9)/(x^2-12x+3) Find all values of x that are NOT in the domain of g. Thank You

Question 636364: The function g is defined below.

g(x)=(x-9)/(x^2-12x+3)

Find all values of x that are NOT in the domain of g.
Thank You
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Hint: set the denominator equal to zero and solve for x. So solve . The easiest way to do this is to use the quadratic formula.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

the domain of is real numbers () the roots of denominator ; as you already know, denominator could NOT be equal to zero.
To find out what they are, solve using quadratic formula:

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-12, and c=3

Negate -12 to get 12

Square -12 to get 144 (note: remember when you square -12, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or

So, all values of that are in the domain of are the solutions

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