Question

Find the range of f(x) = $\frac{1}{1-3\sqrt{1-si{n}^{2}x}}$

Answer 1

Range of $\frac{1}{1-3\sqrt{1-{\sin }^{2}x}}$

$0\le 1-{\sin }^{2}x\le 1$

$0\le 3\sqrt{1-{\sin }^{2}x}\le 3$

$0\ge -3\sqrt{1-{\sin }^{2}x}\ge -3$

$1\ge 1-3\sqrt{1-{\sin }^{2}x}\ge -2$

$1\le \frac{1}{1-3\sqrt{1-{\sin }^{2}x}}\ge -\frac{1}{2}$

$\therefore$ Range $\Rightarrow [-y_2,1]$.