Determine the Domain of the Function: 23 Over (x - 1/4)

Look at the following function:

$\frac{23}{x-\frac{1}{4}}$

What is the domain of the function?

The task is to find the domain of the function $\frac{23}{x-\frac{1}{4}}$.

Let's consider the denominator $x - \frac{1}{4}$. For the function to be defined, this expression should not be equal to zero, since any number divided by zero is undefined.

• Set the denominator equal to zero:

$x - \frac{1}{4} = 0$

• Solve this equation for $x$:

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

This means that when $x = \frac{1}{4}$, the denominator becomes zero, making the function undefined. Therefore, this $x$ value must be excluded from the domain.

Thus, the domain of the function is all real numbers except $\frac{1}{4}$, which can be represented as:

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

This answer matches one of the given choices, specifically choice id="3".

Therefore, the domain of the function $\frac{23}{x-\frac{1}{4}}$ is $x \ne \frac{1}{4}$.