# Difference between revisions of "N-th root"

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:<math> \mathbb{R} \to \mathbb{R}, x \mapsto x^{1/3}</math> | :<math> \mathbb{R} \to \mathbb{R}, x \mapsto x^{1/3}</math> | ||

+ | |||

+ | also for negative values of <math>x</math>. | ||

There are the following choices: | There are the following choices: | ||

− | * "Math.pow(x, 1/3)": this JavaScript function is restricted to positive values of <math>x</math> | + | * "Math.pow(x, 1/3)": this built-in JavaScript function is restricted to positive values of <math>x</math>. |

− | * "JXG.Math.cbrt(x)": cube root function which is able to compute the real cube root of <math>x</math>. It is | + | * "JXG.Math.cbrt(x)": cube root function which is able to compute the real cube root of <math>x</math>. It is available in most browsers as built-in "Math.cbrt()". The JSXGraph makes cbrt available also on old browsers. |

* "JXG.Math.nthroot(x, 3)": general method in JSXGraph to compute the real <math>n</math>-th root of a real number. | * "JXG.Math.nthroot(x, 3)": general method in JSXGraph to compute the real <math>n</math>-th root of a real number. | ||

## Latest revision as of 14:14, 2 April 2020

This example shows the various possibilities to plot the graph of the function

- [math] \mathbb{R} \to \mathbb{R}, x \mapsto x^{1/3}[/math]

also for negative values of [math]x[/math].

There are the following choices:

- "Math.pow(x, 1/3)": this built-in JavaScript function is restricted to positive values of [math]x[/math].
- "JXG.Math.cbrt(x)": cube root function which is able to compute the real cube root of [math]x[/math]. It is available in most browsers as built-in "Math.cbrt()". The JSXGraph makes cbrt available also on old browsers.
- "JXG.Math.nthroot(x, 3)": general method in JSXGraph to compute the real [math]n[/math]-th root of a real number.

### The underlying JavaScript code

```
var board = JXG.JSXGraph.initBoard('jxgbox', {
axis:true,
boundingbox:[-5, 5, 5, -5],
showFullscreen: true
});
var plot1 = board.create('functiongraph', ["nthroot(x, 3)"], {withLabel: true, name:'nthroot(x,3)'});
var plot2 = board.create('functiongraph', ["cbrt(x) + 1"], {withLabel: true, name:'cbrt(x)+1', strokeColor: 'black'});
var plot3 = board.create('functiongraph', [(x) => Math.pow(x, 1/3) - 1], {
withLabel: true,
name:'Math.pow(x, 1/3) - 1',
strokeColor: 'red',
label: {position: 'rt', offset:[-100,-20]}
});
```