Question

State is the following statement is true or false. Give reasons for your answers in the form of a short proof or a counterexample.

The domain of the function f defined by f(x)= √(3-x)/(x-2) is R-{2}.

Answer 1

$$\begin{cases} 3-x\ge0 \\ x-2\not=0 \end{cases}=>x\in(-\infin, 2)\cup(2, 3]$$

Domain: $x\in(-\infin, 2)\cup(2, 3]$

The statement is False.