Calculate the Domain for the Rational Function: 5/(2x - 1/2)

To solve the problem of finding the domain of the function $\frac{5}{2x-\frac{1}{2}}$, we need to ensure the denominator is not zero.

Here is the step-by-step solution:

• Step 1: Identify the denominator of the function, which is $2x - \frac{1}{2}$.
• Step 2: Set the denominator equal to zero: $2x - \frac{1}{2} = 0$.
• Step 3: Solve this equation for $x$:

$2x - \frac{1}{2} = 0$

$2x = \frac{1}{2}$

$x = \frac{1}{4}$

Step 4: The calculated value $x = \frac{1}{4}$ is the value that makes the denominator zero. Hence, the domain of the function consists of all real numbers except $x = \frac{1}{4}$.

Therefore, the domain of the function is all real numbers such that $x \neq \frac{1}{4}$.

The correct choice from the multiple choices is: $x \ne \frac{1}{4}$.

The domain of the function is $x \ne \frac{1}{4}$.