SOLUTION: I am really struggling with this problem. Can someone please help me with it? Thank you so much! Find (f ◦ g)(1), (g ◦ f)(1), (f ◦ g)(x), and (g ◦ f)(x)

Question 227039: I am really struggling with this problem. Can someone please help me with it? Thank you so much!
Find (f ◦ g)(1), (g ◦ f)(1), (f ◦ g)(x), and (g ◦ f)(x) where f(x) = 3x^2 + 4 and g(x) = 4x � 1
Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Find (f ◦ g)(1), (g ◦ f)(1), (f ◦ g)(x), and (g ◦ f)(x) where f(x) = 3x^2 + 4 and g(x) = 4x � 1

well first we find (f ◦ g)(x). To do this we plug in g(x) every time we find an x in f(x).

(f ◦ g)(x) = 3(4x-1)^2+4.

Now we just simplify. I will leave this up to you but you should end up with 48x^2-24x+7.

Now we find (g ◦ f)(x). To do this we plug in f(x) every time we find an x in g(x).

(g ◦ f)(x) = 4(3x^2+4) - 1

Now we just simplify. Again I will leave this for you to do but you should end up with 12x^2+15.

Next we Find (f ◦ g)(1). To do this we plug 1 in for x.

(f ◦ g)(1) = 48(1)^2-24(1)+7 = 48-24+7 = 31

Last we find (g ◦ f)(1). To do this we plug 1 in for x.

(g ◦ f)(1) = 12(1)^2+15 = 12+15 = 27

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SOLUTION: I am really struggling with this problem. Can someone please help me with it? Thank you so much! Find (f &#9702; g)(1), (g &#9702; f)(1), (f &#9702; g)(x), and (g &#9702; f)(x)

SOLUTION: I am really struggling with this problem. Can someone please help me with it? Thank you so much! Find (f ◦ g)(1), (g ◦ f)(1), (f ◦ g)(x), and (g ◦ f)(x)