Find the Inverse Function F-1 of the Function F $$f ( x ) = 3 \sin x - 2$$

question 164

Multiple Choice

Find the inverse function f-1 of the function f.
- $$f ( x ) = 3 \sin x - 2$$

• A) \(f ^ { - 1 } ( x ) = 3 \sin ^ { - 1 } x - 2\)
• B) \(f ^ { - 1 } ( x ) = \sin ^ { - 1 } \left( \frac { x + 2 } { 3 } \right)\)
• C) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \cos \left( \frac { \mathrm { x } + 2 } { 3 } \right)\)
• D) \(f ^ { - 1 } ( x ) = \sin ^ { - 1 } \left( \frac { x + 3 } { 2 } \right)\)

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Definitions:

F Distribution

A continuous probability distribution that arises in the testing of whether two population variances are equal and in the analysis of variance (ANOVA).

Degrees of Freedom

The number of independent values or quantities that can vary in an analysis without violating any constraints, influencing the flexibility of statistical calculations.

F Statistic

A statistical measure used to analyze the variance among group means in a sample, often used in the context of ANOVA.

ANOVA Table

A tabular representation used in analysis of variance to summarize the sources of variation between groups and within groups.