SOLUTION: Just wondering what I can do on this question. Thanks for the help The composition function f(g(x)) = x^4 + 2x^2 + 1. If g(x) = x^2 then what is f(x)? Once you find f(x), fin

Algebra ->  Functions -> SOLUTION: Just wondering what I can do on this question. Thanks for the help The composition function f(g(x)) = x^4 + 2x^2 + 1. If g(x) = x^2 then what is f(x)? Once you find f(x), fin      Log On


   

Question 930518: Just wondering what I can do on this question. Thanks for the help
The composition function f(g(x)) = x^4 + 2x^2 + 1. If g(x) = x^2 then what is f(x)? Once you find f(x), find the function g(f(x)).

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Replace x^2 in the composition with g(x), based on the definition for g(x).


%28x%5E2%29%5E2%2B2x%5E2%2B1
%28g%28x%29%29%5E2%2B2g%28x%29%2B1
Formally explaining the rest is hard to do; but you see g(x) was used as replacement for the variable of f(x).
highlight%28f%28x%29=x%5E2%2B2x%2B1%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Just wondering what I can do on this question. Thanks for the help
The composition function f(g(x)) = x^4 + 2x^2 + 1. If g(x) = x^2 then what is f(x)? Once you find f(x), find the function g(f(x)). 
highlight_green%28f%28x%29+=+x%5E2+%2B+2x+%2B+1%29



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