How do you find $[f o g] (x)$ $[fog](x)$ and $[g o f] (x)$ $[gof](x)$ given $f (x) = x - 4$ $f(x)=x-4$ and $g (x) = 3 x^{2}$ $g(x)=3x^2$ ?

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Answer 1 · 2017-03-05T16:58:27

The answers are
$[f o g] (x) = 3 x^{2} - 4$ $[fog] (x) =3x^2-4$
$[g o f] (x) = 3 {(x - 4)}^{2}$ $[gof] (x)=3(x-4)^2$

This is a composition of functions

$f (x) = x - 4$ $f(x)=x-4$

$g (x) = 3 x^{2}$ $g(x)=3x^2$

$[f o g] (x) = f (g (x)) = f (3 x^{2}) = 3 x^{2} - 4$ $[fog] (x) =f(g(x))=f(3x^2)=3x^2-4$

$[g o f] (x) = g (f (x)) = g (x - 4) = 3 {(x - 4)}^{2}$ $[gof] (x)=g(f(x))=g(x-4)=3(x-4)^2$

How do you find [fog](x)[fog](x)[fog](x) and [gof](x)[gof](x)[gof](x) given f(x)=x-4f(x)=x−4f(x)=x-4 and g(x)=3x^2g(x)=3x2g(x)=3x^2?