SOLUTION: Given f(x) =3x g(x)= 5x^2 +3�..find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0)

Question 984985: Given f(x) =3x
g(x)= 5x^2 +3�..find the following expressions.
(a) (fog)(4)
(b) (gof)(2)
(c) (fof)(1)
(d) (gog)(0)

Answer by farohw(175) (Show Source): You can put this solution on YOUR website!

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

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