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2. domain

If we talk about real functions with real variables:


- The domain of a polynomial function is always R.


Example: f(x) = 3x5 – 5x +243    Dom f = R


- We have to remove the roots of the denominator of a rational function from its domain.


Example:    

                          
Dom f = R – {-2,2}


- The domain of an irrational function f(x) = √R(x) is Dom f = {x,R(x)≥ 0}

Example: f(x) = √(x2 – 3x + 2)

Dom f = (-∞,1]U[2,∞)


- The domain of a logarithmic function  f(x) = loga L(x) is Dom f = {x,L(x)> 0}

Example: f(x) = ln(7x – 21)                
Dom f = (3,∞)

 

 

 

Exercise: find the domain of these functions:

a) f(x) = 3x5- 5x2 - 7x +3

b)   

c)   

d) f(x) = log2 (x2 - 4x + 4)

 

 

Solutions: a) R; b) R - {0, 2, 4}; c) (-∞,-2]U[2,∞); d) R - {2}