Question

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

Answer 1

Answer:

Step-by-step explanation:

➡️Given real function,

➡️f(x) = √(x – 1)

➡️Clearly, √(x – 1) is defined for (x – 1) ≥ 0.

➡️So, the function f(x) = √(x – 1) is defined for x ≥ 1.

➡️Thus, the domain of f is the set of all real numbers greater than or equal to 1.

➡️Domain of f = [1, ∞).

➡️Now,

➡️As x ≥ 1 ⇒ (x – 1) ≥ 0 ⇒ √(x – 1) ≥ 0

➡️Thus, the range of f is the set of all real numbers greater than or equal to 0.

➡️Range of f = [0, ∞).