2210.81 – An Inequality with Radicals

Graph $y_1 = \sqrt{12-x}$ and $y_2 = \sqrt{1+x} + 1$. Below is such a graph from $x = -5$ to $x = 15$. You see that $y_1$ disappears when $x > 12$ and $y_2$ disappears for $x < -1$, when the two quantities stop being real.

As for $y_1 < y_2$? That happens when $3 < x \leq 12$.