Given F(x) and G(x), Find the Indicated Composition and State $g ( x ) = \sqrt { x + 4 }$

question 27

Multiple Choice

Given f(x) and g(x) , find the indicated composition and state its domain.
-For $g ( x ) = \sqrt { x + 4 }$ and $h ( x ) = \frac { 1 } { x - 7 }$ , what is the domain of $h \cdot g$ ?

• A) \([ - 4,7 ) \cup ( 7 , \infty )\)
• B) \([ 0,45 ) \cup ( 45 , \infty )\)
• C) \([ - 4,45 ) \cup ( 45 , \infty )\)
• D) \([ - 4 , \infty )\)

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Definitions:

Holt's Model

A forecasting technique that extends exponential smoothing to allow the data to exhibit a trend.

Observable Trend

A pattern or movement in data over time that can be identified and analyzed to understand current movements and predict future developments.

Seasonality

Regular fluctuations in demand or supply that occur at certain times of the year, often influenced by weather, holidays, or cultural events.

Deseasonalizing

The process of adjusting economic or financial data to eliminate the effects of seasonal variations, facilitating a clearer comprehension of underlying trends.