Question

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

Answer 1

Apply definition. See below

Explanation:

`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