1. 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) = log_a 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) = ln(x²-3x + 2)

Solutions: a) (-∞,1)U(2,∞); b) R-{0,2}