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Question 469265: Let g(x)=2x^2-4. If (f of g)(x)=x^2-4, find f(x).
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Let g(x)=2x^2-4. If (f of g)(x)=x^2-4, find f(x)
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I don't know a clean algebraic way to come up with the answer, but I can do it sort of by trial and error.
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Try f(x)=x
(fog)(x)=2x^2-4
looks like if we cut x in half we will get closer to (fog) but we must also halve -4 so we should add back -2.
2nd try, f(x)=x/2-2
(fog)(x)=((2x^2-4)/2)-2
(fog)(x)=x^2-2-2=x^2-4
ans:
f(x)=x/2-2
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