Given x o y = xy-x-y+2 and f(x) = x+1 , prove that f(xy) = f(x) o f(y).

We'll write f(xy) = xy+1

Now, we'll
manage the right side:

f(x) o
f(y)=(x+1)o(y+1)

We'll apply the rule of composition of 2 terms
:

(x+1)o(y+1)=(x+1)(y+1)-(x+1)-(y+1)+2

(x+1)o(y+1)=xy+x+y+1-x-1-y-1+2

(x+1)o(y+1)=xy+1=f(xy)

We
notice that managing both sides, we've get the same
result.

There fore, the identity f(xy)=f(x)of(y) is
verified.