1.

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

Answer» The given real function is f(x) = √( x− 1)
It can be seen that √( 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

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,∞).


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