To find: Solve for x in the interval \(\displaystyle{\left[-{3},{3}\right]}\) 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 \(\displaystyle{\left\lbrace-{1},{0},{1}\right\rbrace}.\)

\(\displaystyle{x}^{{\frac{1}{{3}}}}-{x}={0}\)

\(\displaystyle\Rightarrow{x}^{{\frac{1}{{3}}}}={x}\)

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 \(\displaystyle{\left\lbrace-{1},{0},{1}\right\rbrace}.\)