Given F(x) = 3x+1, G(x) = 2x, #H(x) = x^2#, how do you find the rule for (F o (G o H) )(x)?

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Answer 1 · 2017-12-14T14:07:14

The answer is #=6x^2+1#

The functions are

#f(x)=3x+1#

#g(x)=2x#

#h(x)=x^2#

#(goh)(x)=g(h(x))=g(x^2)=2x^2#

Therefore,

#fo(goh)(x)=f(g(h(x)))=f(g(x^2))=f(2x^2)=3(2x^2)+1#

#=6x^2+1#