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