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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: set the denominator equal to zero and solve for x. So solve x%5E2-12x%2B3=0. The easiest way to do this is to use the quadratic formula.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

g%28x%29=%28x-9%29%2F%28x%5E2-12x%2B3%29

the domain of g%28x%29 is all real numbers (R) except the roots of denominator x%5E2-12x%2B3; 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


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-12%2Ax%2B3=0 ( notice a=1, b=-12, and c=3)





x+=+%28--12+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29 Plug in a=1, b=-12, and c=3




x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29 Negate -12 to get 12




x+=+%2812+%2B-+sqrt%28+144-4%2A1%2A3+%29%29%2F%282%2A1%29 Square -12 to get 144 (note: remember when you square -12, you must square the negative as well. This is because %28-12%29%5E2=-12%2A-12=144.)




x+=+%2812+%2B-+sqrt%28+144%2B-12+%29%29%2F%282%2A1%29 Multiply -4%2A3%2A1 to get -12




x+=+%2812+%2B-+sqrt%28+132+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2812+%2B-+2%2Asqrt%2833%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2812+%2B-+2%2Asqrt%2833%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2812+%2B+2%2Asqrt%2833%29%29%2F2 or x+=+%2812+-+2%2Asqrt%2833%29%29%2F2



Now break up the fraction



x=%2B12%2F2%2B2%2Asqrt%2833%29%2F2 or x=%2B12%2F2-2%2Asqrt%2833%29%2F2



Simplify



x=6%2Bsqrt%2833%29 or x=6-sqrt%2833%29



So the solutions are:

x=6%2Bsqrt%2833%29 or x=6-sqrt%2833%29





So, all values of x that are NOT in the domain of g are the solutions
x=6%2Bsqrt%2833%29 and x=6-sqrt%2833%29