Question

Find the domain of the function. $$y=\frac{3}{2-x}$$

Short answer

The domain of the function \(y=\frac{3}{2-x}\) is all real numbers except 2.

Step-by-step solution

Identify the function

Look at the function \(y=\frac{3}{2-x}\) and recognize that it is a rational function, where the numerator is 3 and the denominator is 2-x.

Set Denominator Equal to Zero

Set the denominator equal to zero and solve it. Therefore, set 2 - x = 0. Solving for x gives x = 2.

Determine the Domain

Since a function is undefined when the denominator equals zero, the domain consists of all real numbers except the value that makes the denominator zero. In this case, the function is undefined when x = 2. Therefore, the domain of the function \(y=\frac{3}{2-x}\) is all real numbers except 2.