Answer
$x=\pm \frac{1}{\sqrt{3}}$ or $x\approx \pm 0. 557$
Work Step by Step
$\tan^{-1}(3x^2)=\frac{\pi}{4}$ (Use the property $\tan^{-1}(x)=y\Leftrightarrow x=\tan (y)$)
$3x^2=\tan\frac{\pi}{4}$
$3x^2=1$ (Divide by 3)
$x^2=\frac{1}{3}$
$x=\pm \frac{1}{\sqrt{3}}$
$x=\pm 0.57735...$
$x\approx \pm 0.577$
Thus, $x=\pm \frac{1}{\sqrt{3}}$ or $x\approx \pm 0. 557$.
