Question

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

Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

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

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

➡️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, ∞).

Answer 2

Answer:

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

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\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }∣ANSWER∣

➡️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, ∞).