Question

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

Answer 1

No it is not R-{2}

$domain \space of\space\frac{\sqrt{3-x}}{\sqrt{x-2}}:\space= \begin{bmatrix} solution: & 2 \lt\ x\leq 3 \\ interval\space notation: &( 2,3\rbrack \end{bmatrix}$

$domain \ set\ builder \ notation=2 \lt\ x\leq 3$

$domain=(2,3]$