Consider the function f(x) = sqrt(2x - 1) / (x^2 - 3x - 4). What is the domain of f?
Show the answer and explanation
Correct answer
A. [1/2, 4) ∪ (4, ∞)
Principle or equation
The domain of a function includes all real numbers for which the expression is defined. For a square root, the radicand must be nonnegative. For a rational function, the denominator cannot be zero.
Why this answer is correct
The radicand 2x - 1 must be ≥ 0, so x ≥ 1/2. The denominator factors as (x - 4)(x + 1), so x ≠ 4 and x ≠ -1. Since x ≥ 1/2, the value -1 is not in the domain anyway. Thus the domain is [1/2, 4) ∪ (4, ∞).
Example
For f(x) = sqrt(x - 2)/(x - 3), domain is [2, 3) ∪ (3, ∞).
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