Question

y = x+3÷x^2 +2 find domain and range

Answer 1

$y = \frac{(x + 3)}{ {x}^{2} + 2} \\ for \: domain \: check \: for \: which \\ value \: of \: x \: function \: is \: defined$
for each and every value of x ,function is defined,so domain:R
for range we have to write the equation in terms of x
$y( {x}^{2} + 2) = x + 3 \\ y {x}^{2} + 2y - x = 3 \\ y {x}^{2} - x = 3 - 2y$
x can not be represented entirely in the form of Y only,but from here you can check that for every value of Y there exit function x.so range is also entire REAL NUMBER.