Question 380268: I kind of understand how functions work but this is just confusing and I dont understand if the circles mean to multiply or what. Can you help me solve this problem and understand so that I can study for my test.
f and g are functions from R to R.
Consider f(x) = 3x+7, g(x) = x^{2}.
f o g =___ g o f =___
Consider f(x) = sqrt{x^2+3}, g(x) = x^2+5.
f o g =___ g o f = ___
Answer by Jk22(389)   (Show Source):
You can put this solution on YOUR website! IF we have 2 functions f(x), g(x), o is called composition of function, we have :
(fog)(x)=f(g(x))
Consider f(x) = 3x+7, g(x) = x^{2}.
f o g = 3g(x)+7 = 3x^2 + 7
g o f = (3x+7)^2 = 9x^2 + 42x + 49
This can be done in 2 steps :
Consider f(x) = sqrt{x^2+3}, g(x) = x^2+5.
(f o g)(x) = sqrt(y^2+3), y=x^2+5=g(x), hence
= sqrt((x^2+5)^2+3) = sqrt(x^4 + 10x^2 + 28)
(g o f)(x) = g(y), with y=f(x)
=(y^2+5) = (f(x)^2+5) = x^2+8
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