find domain of f(x)=3/x+5 + 2radical x-1
To find the domain of the function f(x) = 3/x + 5 + 2√(x - 1), we need to identify any values of x that would result in undefined expressions.
Starting with the denominator of the first term in the function, we see that it is x. To avoid division by zero, we require x ≠ 0.
Next, considering the square root term, we need to ensure that the radicand (x - 1) is non-negative. In other words, x - 1 ≥ 0. This inequality can be solved by adding 1 to both sides, giving us x ≥ 1.
Combining these conditions, the domain of the function is all real numbers x such that x ≠ 0 and x ≥ 1.
In interval notation, the domain can be expressed as (1, ∞) U (-∞, 0) U (0, 1).