They key is to understand the meaning of domain. For all values of x for which f(x) is a real number a set of such value is called the domain.

So try and find things like values where the function is imaginary or a point where the value of f(x) suddenly goes to infinity.

Case no 4 i your question is example of imaginary value of f(x).

Example of a function suddenly going to infinity is \(f(x)= \frac{1}{x}\) Here domain of f(x) is all real number except x=0.


1) f(x) = -4
This is constant function, ie for any value of x you will have a constant value of y so f(x) is defined for all real values of x.

Thus domain of this is the set of all real numbers R.


2) f(x) = 100 - 900x
This is a sum of a constant and a linear function. Both functions are defined for all real numbers

Thus domain of this is the set of all real numbers R.

3) f(x) = 5 - (x+20)^2
This is a sum of a constant and quadratic function. Both functions are defined for all real numbers

Thus domain of this is the set of all real numbers R.


4) f(x) = \(\sqrt{x+2}\)

Here is x < -2 then f(x) is undefined. for any other value f(x) is defined.

Here the domain x all values of \(x \geq -2\).

5) f(x) = x + |x|

This is a sum of a constant and modulous function. Both functions are defined for all real numbers

Thus domain of this is the set of all real numbers R.