Problem 77 - College Algebra Essentials

Question

Find the domain of each logarithmic function. $$f(x)=\log (2-x)$$

Step-by-Step Solution

Answer

The domain of the function \(f(x) = \log(2 - x)\) is \(x < 2\).

Step 1: Identify the function

The given function is \(f(x) = \log(2 - x)\). The domain will be the set of x-values for which this function is defined.

Step 2: Set the Function's Argument to Greater than Zero

For a function to be defined in logarithm, the argument of the logarithm must be greater than zero. Therefore, set \(2 - x\) greater than zero: \(2 - x > 0\)

Step 3: Solve for x

Rewrite the equation \(2 - x > 0\) to solve for x. When x is subtracted from both sides, the inequality is reversed to \(x < 2\). This means all x values should be less than 2 for the function to be defined.