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 of its domain.

 Example:

         Dom f = R – {-2,2}

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

Example: f(x) = √(x² – 3x + 2)            Dom f = (-∞,1]U[2,∞)

Exercise: find the domain of these functions:

a) f(x) = 3x⁵- 5x² - 7x +3

b)   

c)   

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