How do you find [f • g](x) and [g • f](x) if $F(x) = x^2 - 1$ and $g(x) = -4x^2$ ?

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Answer 1 · 2015-11-04T19:55:14

By definition,

$(f@g)(x)=f[g(x)]=f(-4x^2)$

$=(-4x^2)^2-1=16x^4-1$

Similarly, $(g@f)(x)=g[f(x)]$

$=g(x^2-1)=-4(x^2-1)^2$

How do you find [f • g](x) and [g • f](x) if F(x) = x^2 - 1F(x) = x^2 - 1 and g(x) = -4x^2g(x) = -4x^2?