Question

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

Answer 1

The domain of the function is the set of the all values of the argument where the function exists.

In the given case: $f(x)={\frac{\sqrt{3-x}} {x-2}}$

The function exists when $3-x≥ 0$ and $(x-2)\not=0$

So, the domain is $x\in (-\infty;3]$\ {2}, not R \ {2}