Question

Find the domain and the range of the real function f defined by \(f(x)=\sqrt {(x-1)}\)

Answer 1

The given real function is .\(f(x)=\sqrt{x-1}\)
It can be seen that \(\sqrt{x-1}\) is defined for (x-1) ≥0.
i.e., \(f(x)=\sqrt{x-1}\) 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 
⇒\(\sqrt{x-1}\) ≥ 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,∞).