Question

Find the Domain and Range of the real function f(x) = √25-x²​

Answer 1

Answer:

Given below.

Step-by-step explanation:

⇒ √( 25 - x^2 )

     For all real solutions, √( 25 - x^2 ) must be a real number.

⇒ √( 25 - x )^2 ≥ 0

⇒ 25 - x^2 ≥ 0

⇒ 25 ≥ x^2

⇒ ± 5 ≥ x

     Domain is { - 5 , - 4 , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 , 5 }.

Let a = √( 25 - x )^2

⇒ a^2 = 25 - x^2

⇒ x^2 = 25 - a^2

⇒ x = √( 25 - a^2 )

⇒ x = a real number greater than 0.

⇒ x lies between 0 and + 5.

     Range is { 0 , 1 , 2 , 3 , 4 , 5 }