Solve the equation graphically in the given interval. State each answer rounded to two decimals. displaystyle{x}^{{frac{1}{{3}}}}-{x}={0},{left[-{3},{3}right]} x = ?

To find: Solve for x in the interval ${\displaystyle [-3,3]}$ graphically,
${\displaystyle x^{\frac{1}{3}}-x=0}$
${\displaystyle \Rightarrow x^{\frac{1}{3}}=x}$
In order to solve graphically, we plot say ${\displaystyle y=x^{\frac{1}{3}}\text{and}z=x}$ and find the points where the two graphs intersect.

From the graph it is clear that the graphs intersect at three points. That is, $x=-1,x=0\text{and}x=1$ which are the solution for the given equation.
Hence, solution set is ${\displaystyle \{-1,0,1\}.}$