Determine the domain of f(x) = sqrt(2x + 3).

Prepare for the TSI A2 Mathematics Test. Enhance your skills with comprehensive questions, detailed solutions, and effective strategies. Succeed on your exam!

Multiple Choice

Determine the domain of f(x) = sqrt(2x + 3).

Explanation:
For a real square root, the expression inside must be nonnegative. So for f(x) = sqrt(2x + 3), require 2x + 3 ≥ 0. Solving gives x ≥ -3/2. This means all real numbers at or to the right of -3/2 are allowed, i.e., the domain is [-3/2, ∞). If x < -3/2, the inside is negative and the square root isn’t real, which is why those values aren’t in the domain. The boundary value -3/2 works because it makes the radicand zero, giving f(x) = 0.

For a real square root, the expression inside must be nonnegative. So for f(x) = sqrt(2x + 3), require 2x + 3 ≥ 0. Solving gives x ≥ -3/2. This means all real numbers at or to the right of -3/2 are allowed, i.e., the domain is [-3/2, ∞). If x < -3/2, the inside is negative and the square root isn’t real, which is why those values aren’t in the domain. The boundary value -3/2 works because it makes the radicand zero, giving f(x) = 0.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy