# Find the Domain and Range of the Following Real Function: F(X) = Sqrt(9 - X^2) - Mathematics

Sum

Find the domain and range of the following real function:

f(x) = sqrt(9 - x^2)

#### Solution

f(x) = sqrt(9 - x^2)

Since sqrt(9 - x^2) is defined for all real numbers that are greater than or equal to –3 and less than or equal to 3, the domain of f(x) is {x : –3 ≤ x ≤ 3} or [–3, 3].

For any value of x such that –3 ≤ x ≤ 3, the value of f(x) will lie between 0 and 3.

∴The range of f(x) is {x: 0 ≤ x ≤ 3} or [0, 3].

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#### APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 2 Relations and Functions
Exercise 2.3 | Q 2.2 | Page 44