SOLUTION: Given f(x) = x^3 and g(x) = 3+6x^2, find (g o f) (x).

Question 29813: Given f(x) = x^3 and g(x) = 3+6x^2, find (g o f) (x).

Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Given f(x) = x^3 and g(x) = 3+6x^2, find (g o f) (x).
f(x) = x^3 ----(1)
g(x) = 3+6x^2 ----(2)
(1) and (2) being polynomials in x are defined for all x
To find (gof)(x)
(gof)(x)= g(f(x))
=g(x^3) (using (1))
=g(t) where t = x^3
=3+6t^2 (using (2)
=3+6[(x^3)^2] (putting t back)
=3+6x^6
=3(1+2x^6) which is defined for all x.

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