Question

Find the domain and the range of the real function f defined by.

Answer 1

The given real function is.

It can be seen that is defined for (x – 1) ≥ 0.

i.e., 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 ⇒

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,).