Find the domain of f(x)=(sqrt (x-2))/(2x-5)
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To find the domain of a function, you need to determine all the values of x for which the function is defined.
In this case, we have the function f(x) = √(x-2) / (2x-5).
To determine the domain, we need to consider two things:
1. The square root: The radicand (the expression inside the square root) must be non-negative. In other words, x-2 ≥ 0, because we can't take the square root of a negative number. Solving this inequality, we have x ≥ 2.
2. The denominator: The denominator (2x-5) cannot equal zero because dividing by zero is undefined. So, we set the denominator equal to zero and solve for x: 2x-5 = 0. Adding 5 to both sides, we have 2x = 5, and dividing both sides by 2, we get x = 2.5.
Therefore, the domain of the function is all real numbers greater than or equal to 2, except x = 2.5.
In interval notation, the domain can be expressed as [2.5, ∞) U [2, ∞).