Following are main examples of domain of functions :-

**1. Find the domain of function :-**

f(x) = Square root of - x

For f(x) to be real,

-x >= 0, x=< 0

Df = Set of all real less than or equal to zero.

= (- ∞, 0)

**2. Find the domain of**

f(x) = 1 / (x-1)

For f to be defined

x - 1 not equal to 0, i.e. x not equal to 1

Domain of function is set of all real numbers except 1

**3. Find the domain of**

g(x) = log (x - 1)

For f to be defined,

X - 1 > 0 i.e. X > 1

( Because log of a + ve number only is defined )

So, Df is set of all real and greater than 1

**4. Find the domain of**

f(x) = 1 / (x -1)(x -2)

For Df, f(x) is a real number if x is a real number except 1 and 2

**5. Find the domain of**

f(x) = - Square root of ( -5 -6x - x^2)

For f(X) to be real

-5 -6x - x^2 >= 0

x^2 + 6x +5 =< 0

x^2 + 6x =< -5

x^2 +6x +9 =< 9-5

(X+3) ^2 =< 4

| x+3| ^2 =< 2^2

| x+3| =< 2

Now,

-(x+3)= < 2

- x -3 =< 2

- x =<5 nbsp="">

x>= -5

(x+3)= < 2

x=<2 nbsp="">

x=< -1

Domain of function Df = { -5, -1}

**Same example, you can learn from following video tutorial**