Given $F (x) = 3 x + 1, G (x) = 2 x, H (x) = x^{2}$ $F(x) = 3x+1, G(x) = 2x, H(x) = x^2$ , how do you find the rule for $((F \circ G) \circ H) (x)$ $((F @ G) @ H) (x)$ ?

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Answer 1 · 2017-04-27T12:58:16

$((F o G) o H) (x) = 6 x^{2} + 1 .$ $((FoG)oH)(x)=6x^2+1.$

$F (x) = 3 x + 1, G (x) = 2 x, and, H (x) = x^{2} .$ $F(x)=3x+1, G(x)=2x, and, H(x)=x^2.$

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

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

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

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

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

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

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

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

Given F(x) = 3x+1, G(x) = 2x, H(x) = x^2F(x)=3x+1,G(x)=2x,H(x)=x2F(x) = 3x+1, G(x) = 2x, H(x) = x^2, how do you find the rule for ((F @ G) @ H) (x)((F∘G)∘H)(x)((F @ G) @ H) (x)?