# Find the domain and range of the following real functions (i) f (x) = - |x| (ii) f (x) = √( 9 - x^{2})

**Solution:**

(i) f (x) = - |x| x ∈R

We know that, |x| = {x, if x ≥ 0; - x if x < 0}

Therefore, f (x) = |- x| = {- x, if x ≥ 0; x if x < 0}

Since f (x) is defined for x Î R, the domain of f = R

It can be observed that the range of f ( x) = - |x| is all real numbers except positive real numbers.

Therefore,

the range of is f = (- ∞, 0)

(ii) f (x) = √( 9 - x^{2})

Since√( 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.

Therefore, the range of f (x) is {x : 0 ≤ x ≤ 3} or [0, 3]

NCERT Solutions Class 11 Maths Chapter 2 Exercise 2.3 Question 2

## Find the domain and range of the following real function (i) f (x) = - |x| (ii) f (x) = √( 9 - x^{2})

**Summary:**

Two functions are given. We have found that the range of f (x) is {x : 0 ≤ x ≤ 3} or [0, 3] and the domain of f (x) is {x : - 3 ≤ x ≤ 3} or [- 3, 3]