For the Function F, Use Composition of Functions to Show $\mathrm { f } ^ { - 1 } \text { is as given. }$

question 38

Essay

For the function f, use composition of functions to show that f $\mathrm { f } ^ { - 1 } \text { is as given. }$
- $$f ( x ) = \sqrt [ 3 ] { x + 3 } , f ^ { - 1 } ( x ) = x ^ { 3 } - 3$$

---

Definitions:

Standard Deviation

A statistic that measures the dispersion or variability of a dataset relative to its mean, indicating how spread out the numbers are.

Normally Distributed

Refers to a type of distribution where the data points are symmetrically distributed around the mean, with most observations clustering around the central peak and the probabilities for values further from the mean tapering off equally in both directions.

Mean

The mean of a collection of numbers, determined by dividing their total sum by the count of the numbers.

Standard Deviation

A gauge for the level of dispersion or spread within a set of data points, indicating the magnitude of deviation from the mean.