For f(x) = 4 – x and g(x) = 2x + x + 7, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (g of)(2) (Simpl

Question

For f(x) = 4 – x and g(x) = 2x + x + 7, find the following functions.
a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (g of)(2)
(Simplify your answer.)
solve for each

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Genesis 5 days 2022-01-14T11:44:02+00:00 1 Answer 0 views 0

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    2022-01-14T11:45:19+00:00

    Answer: a. -3(x+1), b. 19-3x, c. -9 and d. 13

    Step-by-step explanation:

    Lets begin with a.  (fog)(x)=f(g(x))

                                                 =f(2x+x+7), Note that 2x+x+7=3x+7

                                                 =f(3x+7) (where there  is x if the function f(x) we

                                                   substitute x by 3x+7)

                                                 =4-(3x+7) =4-3x-7=-3x-3= -3(x+1).

                                b. (gof)(x)=g(f(x))=g(4-x) (where there is x in the function  

                                                    g(x) we substitute with 4-x)

                                                 = 3(4-x)+7 = 19-3x

                              c.  (fog)(2) = -3(2+1) = -9 (we now substitute x with 2 in -3(x+1). )

                               d. (gof)(2) = 19-3(2)=19-6=13. (Again we now substitute x with

                                                   2 in 19-3x)

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