Find the domain of the function. $$ y(x)=\frac{4}{7-4 x} $$ Choose the correct domain below. A. $$ \{x \mid x $$ is a real number and $$ x
eq 4\} $$ B. $$ \{x \mid x $$ is a real number and $$ x
eq 0\} $$ C. $$ \left\{x \mid x ight. $$ is a real number and $$ \left.x \geq \frac{7}{4} ight\} $$ D. $$ \left\{x \mid x ight. $$ is a real number and $$ \left.x
eq \frac{7}{4} ight\} $$

Question

Find the domain of the function. $$ y(x)=\frac{4}{7-4 x} $$ Choose the correct domain below. A. $$ \{x \mid x $$ is a real number and $$ x 
eq 4\} $$ B. $$ \{x \mid x $$ is a real number and $$ x 
eq 0\} $$ C. $$ \left\{x \mid xight. $$ is a real number and $$ \left.x \geq \frac{7}{4}ight\} $$ D. $$ \left\{x \mid xight. $$ is a real number and $$ \left.x 
eq \frac{7}{4}ight\} $$

UpStudy AI · Accepted Answer

To determine the domain of the function $$ y(x) = \frac{4}{7 - 4x} $$, we need to identify all real numbers $$ x $$ for which the function is defined.

The function is undefined when the denominator is zero because division by zero is undefined. Therefore, we set the denominator equal to zero and solve for $$ x $$:

$$
7 - 4x = 0
$$

$$
4x = 7
$$

$$
x = \frac{7}{4}
$$

So, the function $$ y(x) $$ is undefined at $$ x = \frac{7}{4} $$. This means that the domain of the function includes all real numbers except $$ x = \frac{7}{4} $$.

**Answer:**  
D. $$ \left\{x \mid x\right. $$ is a real number and $$ \left.x \neq \frac{7}{4}\right\} $$
The domain of the function is all real numbers except $$ x = \frac{7}{4} $$.

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