Hello,

Well, let's first care of gof=g(f(x))

Distinguish two situations :

- x>0 : f(x)=x ---> g(f(x))=e^x

- x<0 : f(x)=1/x ---> g(f(x))=e^(1/x)

Now let's care of fog=f(g(x))

Write f(t)=t if t>0, =1/t if t<0

Consider g(x)=t. It's often useful when dealing with composite functions.

So when t=g(x) is positive, then f(t)=t.

When t=g(x) is negative, then f(t)=1/t.

But e^x ispositivefor any x.

Then g(x)=e^x=t>0 ---> f(g(x))=t=e^x

Does it look clear ?