How do you find $[f o g] (x)$ $[fog](x)$ and $[g o f] (x)$ $[gof](x)$ given $f (x) = 2 x$ $f(x)=2x$ and $g (x) = x^{3} + x^{2} + 1$ $g(x)=x^3+x^2+1$ ?

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Answer 1 · 2017-03-06T22:18:42

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$f g (x) = f (x^{3} + x^{2} + 1) = 2 x^{3} + 2 x^{2} + 2$ $fg(x)=f(x^3+x^2+1)=2x^3+2x^2+2$

$g f (x) = g (2 x) = {(2 x)}^{3} + {(2 x)}^{2} + 1 = 8 x^{3} + 4 x^{2} + 1$ $gf(x)=g(2x)=(2x)^3+(2x)^2+1=8x^3+4x^2+1$

How do you find [fog](x)[fog](x) and [gof](x)[gof](x) given f(x)=2xf(x)=2x and g(x)=x3+x2+1g(x)=x^3+x^2+1?