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

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)