Question

What is the domain of the rational function f(x) = (3x) / (2x^3 - x^2 - 15x)?

A) All real numbers except x = 0
B) x < 0 or x > 5
C) x ≠ -3, 0, 5
D) All real numbers

Answer 1

The domain of the rational function f(x) = (3x) / (2x^3 - x^2 - 15x) is C) x ≠ -3, 0, 5.

Step-by-step explanation:

The domain of the rational function f(x) = (3x) / (2x^3 - x^2 - 15x) is C) x ≠ -3, 0, 5.

To find the domain, we need to consider the values of x that would make the denominator zero, as division by zero is undefined. So, we set the denominator equal to zero and solve for x.

2x^3 - x^2 - 15x = 0

Factorizing the equation, we get: (x+3)(x-5)(2x+1) = 0

Therefore, x cannot be equal to -3, 0, or 5. This restriction on x gives us the domain of the function.