Let `f` be the cosine function and let `g` be the function `x^2`. Find
(i) `fog` (ii) `gof` (iii) `fof` (iv) `gog`

Explanation

We have `f(x)=cosx` and `g(x)=x^2`
(i) `(fog)(x)=f(g(x))=f(x^2)=cos x^2`
(ii) `(gof)(x)=g(f(x))=g(cos x) = cos x^2`
(iii) `(fof)(x)=f(f(x))=f(cosx)=cos(cosx)`
(iv) `(gog)(x)=g(g(x))=g(x^2)=(x^2)^2=x^4`