Question

Solve the following inequality:

${\left(\frac{1}{3}\right)}^{\sqrt{x+2}}>3^{-x}$

Answer 1

$(\frac{1}{3}{)}^{\sqrt{x+2}}>3^{-x}$

$3^{-\sqrt{x+2}}>3^{-x}$

$-\sqrt{x+2}>-x⟹\sqrt{x+2}<x⟹x^2-x-2>0⟹x\in (-\infty ,-1)\cup (2,\infty )$

and $x+2\ge 0⟹x\ge -2$

So $x\in [-2,-1)\cup (2,\infty )$