Find the domain and the range of the real function f defined by f(x)=√(x−1)
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Solution
The given real function is f(x)=√x−1 It can be seen that √x−1 is defined for (x−1)≥0 i.e., f(x)=√(x−1) is defined for x≥1 Therefore the domain of f is the set of all real numbers greater than or equal to 1 i.e., the domain of f =[1,∞)
As x≥1
⇒(x−1)≥0
⇒√x−1≥0
f(x)≥0 Therefore the range of f is the set of all real numbers greater than or equal to 0 i.e., the range of f =[0,∞)