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

Solution:

The given real function is f(x) = √(x - 1)

It can be seen that √(x - 1) is defined for x ≥ 1

The domain of a function is the set of all possible inputs for the function.

The range of a function is the set of all its outputs.

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, ∞)

Hence,

⇒ 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, ∞)

NCERT Solutions Class 11 Maths Chapter 2 Exercise ME Question 4

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

Summary:

A function f defined by f (x) = √ (x - 1) is given. We have found that the domain of f is [1, ∞) and range of f is the set of all real numbers greater than or equal to 0 i.e., the range of f = [0, ∞).