# Find the domain and the range of the real function f defined by () = √( − 1)

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Find the domain and the range of the real function f defined by () = √( − 1)

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The given real function is () = √( − 1) It can be seen that √( − 1) is defined for  ≥ 1.

The given function is  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 ⇒ √( − 1) ≥ 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, ).