Question 984985

Given f(x) = 3x, g(x) = 5x^2 + 3.


a) Since (fog)(x) is f(g(x)) then (fog)(4) is f(g(4)).


Therefore, f(g(x)) ---> f(5x^2 +3) = 3(5x^2 + 3) 


You can choose to simplify by multiplying 3(5x^2 + 3) = 15x^2 + 9 but either way you will get the same answer when you substitute x for 4,


3(5x^2 + 3)= 3(5(4)^2 + 3) = 249  


OR  


15x^2 + 9 = 15(4)^2 + 9 = 249.



b) (gof)(x) = g(f(x)) and g(f(2))


g(f(x)) --> g(3x) = 5(3x)^2 + 3 and,


g(f(2)) is 5(3(2))^2 + 3 --> 5(36) + 3 = 183.



c) (fof)(x) = f(f(x)) and f(f(1))


f(3x) = 3(3x) ---> 3(3(1)) = 9.



I think you can do the last problem, (gog)(x) = g(g(0)).


Hint: g(5x^2 + 3) = 5(5x^2 + 3)^2 + 3 then do substitution and solve.


Best, 
Farohw