Question

Find the domain and range of f(x) = |2x-3|– 3

Answer 1

Given, f(x) = |2 − 3| − 3 

The domain of the expression in all real number expect where the expression is undefined. In this case, there is not real number that makes the expression undefined. 

∴ Domain of f = (− ∞, ∞) = R 

The absolute value of expression has a ‘V’ shape. The range of a positive absolute value expression starts at its vertex and extends to infinity. 

Range of f = [−3, ∞] or {y/y ≥ − 3}