NationalEasyFunctions10–12

Domain of a Radical Quotient

Domínio de um Quociente com Radical

Determine the domain of $f(x) = \dfrac{\sqrt{x - 3}}{x - 5}$ .

Two conditions have to hold at the same time: one comes from the radical, the other from the denominator. Write each as a restriction on $x$ before combining them.

Solution

Step 1 of 4

1.Radical: $x - 3 \ge 0 \Leftrightarrow x \ge 3$