f(1/(x+1))=2x-12.
(i) Let y=1/(x+1), xy+y=1, x=(1-y)/y;
f(y)=2(1-y)/y-12=(2-2y-12y)/y=(2-14y/y=(2/y)-14, which can also be written:
f(x)=(2/x)-14.
so f(0)=2/0-14⇒∞.
(ii) Another way:
If 1/(x+1)=0, then x→∞, so f(0)→∞.
[To find f(2) we have:
(i) f(2)=(2/2)-14=-13
(ii) 1/(x+1)=2, 2x+2=1, x=-½, so f(2)=2(-½)-12=-13.
This shows that the two methods yield the same result.]