How do you find $(gof)(-2)$ given $f(x)=-3x+4$ and $g(x)=x^2$ ?

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Answer 1 · 2018-04-25T12:15:46

Apply definition. See below

$g@f(x)=g(f(x))=g(-3x+4)=(-3x+4)^2$

In $x=-2$ we have $g@f(-2)=(-2·-3+4)^2=10^2=100$

As bonus

$f@g(x)=f(g(x))=f(x^2)=-3x^2+4$

And for $x=-2$ we have $f@g(-2)=-3(-2)^2+4=-8$

So composed functions are not the same and then there is no conmutativity

How do you find (gof)(-2)(gof)(-2) given f(x)=-3x+4f(x)=-3x+4 and g(x)=x^2g(x)=x^2?