Final answer:
To algebraically find the domain and range of √(2x-1), we set the expression inside the square root ≥ 0. The domain is x ≥ 1/2 and the range is all real numbers ≥ 0. Solving √(2x-1) = 0 gives x = 1/2. The values of x for which √(2x-1) is defined are x ≥ 1/2.
Step-by-step explanation:
To algebraically find the domain and range of √(2x-1), we need to consider the restrictions on the function.
(a) The domain refers to the set of values that x can take. In this case, the expression inside the square root, 2x-1, must not be negative or undefined. So we set the inequality 2x-1 ≥ 0 and solve for x. This gives us x ≥ 1/2, which means the domain of the function is all real numbers greater than or equal to 1/2.
(b) The range refers to the set of values that the function can output. The square root function is always non-negative, so the range of √(2x-1) is all real numbers greater than or equal to 0.
(c) To solve for x when √(2x-1) = 0, we set the expression inside the square root equal to zero and solve for x. This gives us 2x-1 = 0, which leads to x = 1/2.
(d) The values of x for which √(2x-1) is defined are the ones that satisfy the domain condition, which is x ≥ 1/2.