Answer
Solution set as $x$-intercepts = $\{ \frac{1}{3},-\frac{1}{2}\}$
The graph of equation $y=x^{-2}-x^{-1}-6$ is shown in Graph$(b)$
Work Step by Step
$y=x^{-2}-x^{-1}-6$
This equation is equivalent to
$y=(x^{-1})^2-x^{-1}-6$
The $y$ coordinate corresponding to an $x$-intercept is zero. So, to find $x$ -intercept, $y=0$
$(x^{-1})^2-x^{-1}-6=0$
Let $(x^{-1})=u$
$u^{2}-u-6=0$
By factoring,
$(u-3)(u+2)=0$
$u=3$ or $u=-2$
Let $u=3$
Replace $u$ with $(x^{-1})$
$(x^{-1})=3$
$\frac{1}{x}=3$
$x = \frac{1}{3}$
Let $u=-2$
$(x^{-1})=-2$
$\frac{1}{x}=-2$
$x = -\frac{1}{2}$
Solution set as $x$-intercepts = $\{ \frac{1}{3},-\frac{1}{2}\}$
The graph of equation $y=x^{-2}-x^{-1}-6$ is shown in Graph$(b)$
