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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