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Step-by-step Answer
PAGE: 388SET: ExercisesPROBLEM: 1
Please look in your text book for this problem Statement

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

a) (f + g)(x)

open parentheses f plus g close parentheses open parentheses x close parentheses equal f open parentheses x close parentheses plus g open parentheses x close parentheses

equal open parentheses 3 x plus 4 close parentheses plus open parentheses 5 plus x close parentheses         (Substitute f(x) = 3x + 4 and g(x) = 5 + x)

equal 4 x plus 9                            (Add: 3 x plus x equal 4 x space italic and space 4 plus 5 equal 9)

b) (f g)(x)

open parentheses f minus g close parentheses open parentheses x close parentheses equal f open parentheses x close parentheses minus g open parentheses x close parentheses

equal open parentheses 3 x plus 4 close parentheses minus open parentheses 5 plus x close parentheses         (Substitute f(x) = 3x + 4 and g(x) = 5 + x)

equal 3 x plus 4 minus 5 minus x

Apply commutative property of addition: .

equal 3 x minus x plus 4 minus 5

equal 2 x minus 1                            (Subtract: 3 x minus x equal 2 x space italic and space 4 minus 5 equal minus 1)

c)open parentheses f times g close parentheses open parentheses x close parentheses

equal open parentheses 3 x plus 4 close parentheses open parentheses 5 plus x close parentheses            (Substitute f(x) = 3x + 4 and g(x) = 5 + x)

equal open parentheses 3 x close parentheses open parentheses 5 close parentheses plus open parentheses 3 x close parentheses open parentheses x close parentheses plus 4 open parentheses 5 close parentheses plus 4 open parentheses x close parentheses  (Using FOIL method)

equal 15 x plus 3 x to the power of 2 plus 20 plus 4 x

equal 3 x to the power of 2 plus 19 x plus 20

d)open parentheses f over g close parentheses open parentheses x close parentheses

open parentheses f over g close parentheses open parentheses x close parentheses equal fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction

equal fraction numerator 3 x plus 4 over denominator 5 plus x end fraction, x not equal to 5               (Substitute f(x) = 3x + 4 and g(x) = 5 + x)

Because x = 5 then 5 + x = 0, minus 5 is excluded from the domain of open parentheses f over g close parentheses open parentheses x close parentheses.



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