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Multiple Choice
Find the domain of the rational function. Then, write it in lowest terms. f(x)=2x2−86x5
A
{x∣x=2,−2},f(x)=x2−43x5
B
{x∣x=2,−2},f(x)=2x2−86x5
C
{x∣x=2},f(x)=x2−43x5
D
{x∣x=2},f(x)=x2−83x5
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1
Identify the rational function given: \( f(x) = \frac{6x^5}{2x^2 - 8} \).
Determine the domain of the function by finding the values of \( x \) that make the denominator zero, since division by zero is undefined.
Set the denominator equal to zero and solve for \( x \): \( 2x^2 - 8 = 0 \).
Factor the equation: \( 2(x^2 - 4) = 0 \), which simplifies to \( x^2 - 4 = 0 \).
Solve \( x^2 - 4 = 0 \) by factoring further: \( (x - 2)(x + 2) = 0 \). The solutions are \( x = 2 \) and \( x = -2 \), so the domain is all real numbers except \( x = 2 \) and \( x = -2 \).