Question

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

Answer 1

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`