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,∞).