Question

Find the domain?

f(x)= root of (2x+3) + whole root of (3-x^2)/x^2

Answer 1

Answer:

Step-by-step explanation:

Domain is the interval of x for which f(x) is defined

$f(x) = \sqrt{2x+3} + \sqrt{\frac{3-x^2}{x^{2} } } \\\\ 2x+3\geq 0 \implies x\geq -\frac{3}{2} ---(1)\\\\ \frac{3-x^2}{x^{2}} \geq0,\ x^2\neq 0 \implies x^2\leq3 \ and \ x\neq0 ---(2) \\\\combining \ (1) \ and \ (2) we get,\\x \ \epsilon \ \left[\frac{-3}{2}, 0 \right)\cup(0,\sqrt{3}]$