Find the Function $f \cdot g$ And Its Domain If $f ( x ) = \sqrt { x + 7 }$

question 143

Multiple Choice

Find the function $f \cdot g$ and its domain if $f ( x ) = \sqrt { x + 7 }$ and $g ( x ) = \sqrt { x - 7 }$ .

• A)
• \(\sqrt { x ^ { 2 } - 49 }\)
• \(D = [ 7 , \infty )\)
• B) \(\sqrt { x ^ { 2 } - 49 }\)
• \[D = [ - 7 , \infty )\]
• C)
• \[\begin{array} { l }
• \sqrt { x ^ { 2 } + 49 } \\
• D = [ - 7 , \infty )
• \end{array}\]
• D) \(\sqrt { x ^ { 2 } + 49 }\)
• \[D = [ 7 , \infty )\]

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Definitions:

Williamson Ether Synthesis

A chemical reaction that synthesizes ethers from alkyl halides and alcohols using a strong base.

Mechanism

A detailed explanation of the step-by-step process by which a chemical reaction occurs.

E2

A bimolecular elimination reaction mechanism where a substrate eliminates two substituents forming a double bond, with the departure of a leaving group and loss of a proton.

Dehydration Reaction

A chemical reaction that involves the removal of water (H2O) from a single reactant, commonly leading to the formation of a double bond in organic compounds.