Questions: g(x)=(5x+3)/(9x-1)

Solution Steps

To find the domain of the function \( g(x) = \frac{5x + 3}{9x - 1} \), we need to determine the values of \( x \) for which the function is defined. The function is undefined when the denominator is zero. Therefore, we need to solve the equation \( 9x - 1 = 0 \) to find the values of \( x \) that make the denominator zero and exclude them from the domain.

The function given is: \[ g(x) = \frac{5x + 3}{9x - 1} \] To find the domain, we need to identify the values of \( x \) that make the denominator zero.

Set the denominator equal to zero and solve for \( x \): \[ 9x - 1 = 0 \] Solving for \( x \): \[ 9x = 1 \implies x = \frac{1}{9} \]

The function \( g(x) \) is undefined at \( x = \frac{1}{9} \). Therefore, the domain of \( g(x) \) includes all real numbers except \( x = \frac{1}{9} \).

Final Answer