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

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Answer 1 · 2016-12-06T15:50:06

The answers are $f@g(x)=2x^2-4x-3$
And $g@f(x)=(2x-3)(2x-5)$

$f(x)=2x-3$

$g(x)=x^2-2x$

$=f(g(x))=f(x^2-2x)=2(x^2-2x)-3$

$=2x^2-4x-3$

$g@f(x)=g(f(x))=g(2x-3)=(2x-3)^2-2(2x-3)$

$=(2x-3)(2x-3-2)$

$=(2x-3)(2x-5)$

$f@g(x)!=g@f(x)$

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