The Function $f ( x ) = \sqrt { x ^ { 2 } - 5 }$

question 17

Multiple Choice

The function $f ( x ) = \sqrt { x ^ { 2 } - 5 }$ is one-to-one on the domain $x \leq - \sqrt { 5 }$ . Find $f ^ { - 1 } ( x )$ .

• A) \(\quad f ^ { - 1 } ( x ) = x ^ { 2 } + 5\)
• B) \(f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 5 }\)
• C) \(f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 5 } }\)
• D) \(\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 5 }\)
• E) \(f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 5 }\)

---

Definitions:

Independent SRSs

Independent Simple Random Samples; a sampling technique where each subset of the population has an equal probability of being chosen, and the selections are made independently of each other.

Normally Distributed

Describing a data set where the observations are symmetrically distributed around the mean, forming a bell-shaped curve.

SSE

SSE, or Sum of Squares Error, is a measure used in statistics to describe the amount of variation or deviation of sample values from the fitted values in a model.

F Statistic

The F statistic is used in statistical testing to compare the variances among group means to decide if they significantly differ from each other.