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teamtommo
So thing of that weird little circle as “of”

Thus: “g of h of x” or g(h(x)). First find h(x) by plugging x in for h and then plug whatever h(x) is in to g.

Ex. If h(x)= 4x + 2 And g(x)= 2x + 5,

g(h(x))= 2(4x + 2) + 5 = 8x + 4 + 5 = 8x + 9

[tex] \bf \begin{cases}
f(x)=x-3\\
g(x)=x^2+1\\
h(x)=-4x+1\\
----------\\
(g\circ h)(x)=g(~~h(x)~~)
\end{cases}
\\\\\\
g(~~h(x)~~)=[h(x)]^2+1\implies g(~~h(x)~~)=[-4x+1]^2+1
\\\\\\
g(~~h(x)~~)=[-4x+1][-4x+1]+1
\\\\\\
g(~~h(x)~~)=\stackrel{FOIL}{[16x^2-8x+1]}+1\implies g(~~h(x)~~)=16x^2-8x+2 [/tex]

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