$\"\"$

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The functions are f(x) = 3x + 4 and g(x) = 5 + x.

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a) (f + g)(x)

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$\"open$

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$\"equal$ (Substitute f(x) = 3x + 4 and g(x) = 5 + x)

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$\"\"$

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$\"equal$ (Add: $\"3$ ) $\"\"$

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b) (f $\"\"$ g)(x)

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$\"open$

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$\"equal$ (Substitute f(x) = 3x + 4 and g(x) = 5 + x)

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$\"equal$

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Apply commutative property of addition: $\"\"$ .

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$\"equal$

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$\"equal$ (Subtract: $\"3$ ) $\"\"$

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c) $\"open$

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$\"\"$

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$\"equal$ (Substitute f(x) = 3x + 4 and g(x) = 5 + x)

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$\"equal$ (Using FOIL method)

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$\"equal$

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$\"equal$ $\"\"$

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d) $\"open$

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$\"open$

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$\"equal$ , $\"x$ (Substitute f(x) = 3x + 4 and g(x) = 5 + x) $\"\"$

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Because x = 5 then 5 + x = 0, $\"minus$ is excluded from the domain of $\"open$ .