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

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Answer 1 · 2017-04-27T12:58:16

# ((FoG)oH)(x)=6x^2+1.#

#F(x)=3x+1, G(x)=2x, and, H(x)=x^2.#

#:. (FoG)(x)=F(G(x)),#

#=3G(x)+1,.......................[because, F(x)=3x+1,],#

#=3(2x)+1,.........................[because, G(x)=2x,],#

#:. (FoG)(x)=6x+1.#

Now, #((FoG)oH)(x)=((FoG))(H(x))#

#=6H(x)+1,..............[because, (FoG)(x)=6x+1,],#

#=6(x^2)+1,................[because, H(x)=x^2,],#

# rArr ((FoG)oH)(x)=6x^2+1.#