Questions: Quiz 1 Find the domain of the function. g(x)=3x/(x^2-25) A. x x>25 B. x x ≠ -5,5 C. all real numbers D. x x ≠ 0

Solution Steps

To find the domain of the function \( g(x) = \frac{3x}{x^2 - 25} \), we need to determine the values of \( x \) for which the function is defined. The function is undefined where the denominator is zero. Therefore, we solve the equation \( x^2 - 25 = 0 \) to find the values of \( x \) that make the denominator zero. These values will be excluded from the domain.

The function given is \( g(x) = \frac{3x}{x^2 - 25} \). To find the domain, we need to identify where the function is undefined. This occurs when the denominator is zero.

Set the denominator equal to zero and solve for \( x \): \[ x^2 - 25 = 0 \] This can be factored as: \[ (x - 5)(x + 5) = 0 \] Solving these equations gives: \[ x = 5 \quad \text{and} \quad x = -5 \]

The function is undefined at \( x = 5 \) and \( x = -5 \). Therefore, the domain of the function is all real numbers except \( x = 5 \) and \( x = -5 \).

Final Answer