Ohio Assessments for Educators (OAE) Mathematics Practice Exam

For the function f(x) = √(ax + b), what is the domain?

1. All real numbers

2. All real numbers where ax + b > 0

3. All real numbers that satisfy ax + b ≤ 0

4. All values of x

The correct answer is: All real numbers where ax + b > 0

The domain of the function \( f(x) = \sqrt{ax + b} \) is determined by the requirement that the expression inside the square root must be non-negative. This is because the square root function is only defined for non-negative numbers in the real number system. To find the domain, you set up the inequality: \[ ax + b \geq 0. \] This means that we need to solve this inequality to find the values of \( x \) for which it holds true. The solution set will provide the values of \( x \) that keep the expression inside the square root non-negative, which is crucial for the output of the function to be real numbers. Therefore, the domain of \( f(x) = \sqrt{ax + b} \) is given by the values of \( x \) that satisfy \( ax + b \geq 0 \). This requirement characterizes option B accurately, as it specifically points out that the function is defined for all real numbers where the expression \( ax + b \) is greater than or equal to zero. The other options do not appropriately reflect this fundamental requirement for defining the domain of the square root function.