Math  /  Algebra

QuestionWhich values are NOT in the domain of the rational function? f(x)=(x1)(x+2)x29f(x) = \frac{(x - 1)(x + 2)}{x^2 - 9}

Studdy Solution

STEP 1

1. The function f(x)=(x1)(x+2)x29 f(x) = \frac{(x - 1)(x + 2)}{x^2 - 9} is a rational function.
2. The domain of a rational function is all real numbers except where the denominator is zero.
3. We need to find the values of x x that make the denominator zero.

STEP 2

1. Identify the denominator of the rational function.
2. Set the denominator equal to zero and solve for x x .
3. List the values of x x that are not in the domain.

STEP 3

Identify the denominator of the rational function:
The denominator of f(x) f(x) is x29 x^2 - 9 .

STEP 4

Set the denominator equal to zero and solve for x x :
x29=0 x^2 - 9 = 0

STEP 5

Solve the equation x29=0 x^2 - 9 = 0 . This is a difference of squares, which can be factored:
(x3)(x+3)=0 (x - 3)(x + 3) = 0
Set each factor equal to zero:
x3=0x=3 x - 3 = 0 \quad \Rightarrow \quad x = 3 x+3=0x=3 x + 3 = 0 \quad \Rightarrow \quad x = -3

STEP 6

List the values of x x that are not in the domain:
The values x=3 x = 3 and x=3 x = -3 make the denominator zero, so they are not in the domain.
The values that are NOT in the domain of the function are 3 \boxed{3} and 3 \boxed{-3} .

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