if f(x)= 3x^2-4x+1 and g(x)=3x^2-3
what values are not in the domain of f/g?
A. 0
B. 1
C. 3
D. +-1
E. no values to exclude
3(x^2-1)3(x+1)(x-1)
(3x-1)(3x-3)
(3x-1) (x-1)
3 x ^ 2 - 4 x + 1 =
( x - 1 ) ( 3 x - 1 )
3 x ^ 2 - 3 =
3 ( x ^ 2 - 1 ) =
3 ( x + 1 ) ( x - 1 )
( 3 x ^ 2 - 4 x + 1 ) / ( 3 x ^ 2 - 3 ) =
( x - 1 ) ( 3 x - 1 ) / [ 3 ( x + 1 ) ( x - 1 ) ] =
( 3 x - 1 ) / [ 3 ( x + 1 ) ] =
1 - 4 / [ ( 3 ( x + 1 ) ]
Domain :
x + 1 # 0
x # - 1
Only point x = - 1 are not in the domain of f / g
so its letter d
To determine the values that are not in the domain of f/g, we need to find the values that make the denominator, g(x), equal to zero.
From the expression g(x) = 3x^2 - 3, we can set it equal to zero and solve for x:
3x^2 - 3 = 0
We can factor out a 3:
3(x^2 - 1) = 0
Now, we have a difference of squares:
3(x + 1)(x - 1) = 0
To find the values that make g(x) equal to zero, we can set each factor equal to zero and solve for x:
x + 1 = 0
x - 1 = 0
Solving these equations, we get:
x = -1
x = 1
Therefore, the values -1 and 1 make g(x) equal to zero. These values are not in the domain of f/g as it would result in division by zero.
So, the values not in the domain of f/g are -1 and 1.
Therefore, the answer is D. +-1