Identify the Domain: Uncovering Restrictions in 3x+4 over 2x-1

Consider the following function:

$\frac{3x+4}{2x-1}$

What is the domain of the function?

To determine the domain of the function $\frac{3x+4}{2x-1}$, follow these steps:

• Step 1: Identify the denominator of the rational function, which is $2x-1$.
• Step 2: Set the denominator equal to zero to find the values of $x$ that make the function undefined:
  $2x - 1 = 0$.
• Step 3: Solve for $x$:
  Add 1 to both sides: $2x = 1$.
  Divide both sides by 2: $x = \frac{1}{2}$.

The value $x = \frac{1}{2}$ makes the denominator zero, which means the function $\frac{3x+4}{2x-1}$ is undefined at $x = \frac{1}{2}$. Therefore, this value must be excluded from the domain.

The domain of the function is all real numbers except $x = \frac{1}{2}$.

Therefore, the solution to the problem is $x \ne \frac{1}{2}$.