For the Given Function, Find the Domain and Range of Both

question 155

Multiple Choice

For the given function, find the domain and range of both f(x) and ${ f } ^ { - 1 } ( \mathrm { x } ) .$
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• A) \(\begin{array} { l } \mathrm { f } : \quad \text { domain: } \{ x \mid x \geq - 4 \} \\ ~~~~\text { range: } \{ \mathrm { y } \mid \mathrm { y } \geq 0 \} \\ \mathrm { f } ^ { - 1 } : \text { domain: } \{ x \mid \mathrm { x } \geq - 4 \} \\ ~~~~\text { range: } \{ \mathrm { y } \mid \mathrm { y } \geq 0 \} \end{array}\)
• B) f: domain: \(\{ x \mid x \geq - 4 \}\) \(~~~~\)range: \(\{ y \mid y \geq 0 \}\) \(\mathrm { f } ^ { - 1 }\) : domain: \(\{ \mathrm { x } \mid \mathrm { x } \geq 0 \}\) \(~~~~\)range: \(\{ y \mid y \geq - 4 \}\)
• C) f: domain: \(\{ x \mid x \geq 0 \}\) \(~~~~\)range: \(\{ y \mid y \geq - 4 \}\) \(\mathrm { f } ^ { - 1 }\) : domain: \(\{ x \mid \mathrm { x } \geq - 4 \}\) \(~~~~\)range: \(\{ y \mid y \geq 0 \}\)
• D) f: domain: \(\{ x \mid x \geq 0 \}\) \(~~~~\)range: \(\{ y \mid y \geq - 4 \}\) \(\mathrm { f } ^ { - 1 }\) : domain: \(\{ \mathrm { x } \mid \mathrm { x } \geq 0 \}\) \(~~~~\)range: \(\{ y \mid y \geq - 4 \}\)

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Definitions:

Ongoing Basis

A continuous or regular manner of operation or occurrence.

Direct Observation Technique

A method of data collection where behaviors or events are recorded by an observer as they happen, without reliance on subject self-reports.

Vertical Axis

In graphing, the y-axis, which is typically used to represent the range of values of the variable being measured.

Horizontal Axis

In graphing, the horizontal line along which the values of one variable are plotted, often representing the independent variable or time.