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The function is $\"\"$ , where $\"\"$ is the molar mass of the gas in kilograms per mole.

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(a) The function is square root function.

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Domain of $\"\"$ is $\"\"$ .

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The molar mass of the gas cannot be negative or zero.

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(b) Find the average speed when $\"\"$ kilograms.

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The average speed is about $\"\"$ meters per second.

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(c)

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As $\"\"$ increase, the value of $\"\"$ also decrease.

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As the molar mass of gas increases, the velocity decreases.

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(d) Decompose the function $\"\"$ .

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One way to write $\"\"$ as a composition of two functions is to let $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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$\"\"$

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Replace $\"\"$ with $\"\"$ .

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$\"\"$

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Substitute $\"\"$ for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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The two functions are $\"\"$ and $\"\"$ .

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(a) Domain is $\"\"$ , the molar mass of the gas cannot be negative or zero.

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(b) The average speed is about $\"\"$ meters per second..

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(c) The velocity will decrease.

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(d) The two functions are $\"\"$ and $\"\"$ .