Question

Find the domain of the function f(x) = 5 / (5-x).

Option 1: All real numbers except x = 5
Option 2: All real numbers except x = -5
Option 3: All real numbers except x = 0
Option 4: All real numbers except x = 1

Answer 1

The domain of the function f(x) = 5 / (5-x) is all real numbers except x = 5, as this value would cause division by zero.

Step-by-step explanation:

To find the domain of the function f(x) = 5 / (5-x), we need to look for the values of x that would make the denominator zero because division by zero is undefined. As the denominator is (5-x), setting it equal to zero gives us 5 - x = 0. Solving for x, we find that x = 5. Hence, the domain of the function is all real numbers except for x = 5, which corresponds to Option 1: All real numbers except x = 5.

To summarize, for a function with a denominator of (5-x), the only value that x cannot take is the one that makes the denominator zero. Since 5 - 5 = 0, the domain of the function excludes only the value x = 5.