Answer
$-1.00$, $0.00$ and $1.00$
Work Step by Step
Given equation-
$x^{\frac{1}{3}} -x$ = $0$ , in the interval [-3,3]
i.e $x^{\frac{1}{3}}$ = $x$
Raising both sides to power '3'-
$x $ = $x^{3}$
i.e. $x^{3} - x $ = $0$ in the interval [-3,3]
We are asked to find all solutions 'x' that satisfy $-3 \leq x \leq 3$, so we use a graphing calculator to graph the equation in a viewing rectangle for which the x-values are restricted to the interval [-3,3] .
Graphing $y$ = $x^{3} - x $, using graphing calculator-
There are three $x-intercepts$ in the given interval, $x= -1.00$, $0.00$ and $1.00$
i.e. $x= -1.00$, $0.00$ and $1.00$
