need help?

Question

the map is f(x) = x+1,

prove that f is homomorphism!
please show steps! thank you.

Answer 1

For G,H as groups, f:G->H is homomorphic if f(a*b) = f(a)f(b) for all a,b in your group G...

Assuming you are using Some group (Z, Q, or R) with addition as your binary operation...

f(x+y) = x+y+1
f(x)f(y) = x+1 + y+1 = x+y+2.
therefore it is not a homomorphism since x+y+1 <> x+y+2.

So it depends on the group and binary operation?

Answer 2

it is even a isomorphism beccause inverse_f(f(x) = x
inverse_f (x) = x-1.

an isomorhism is a homomohism.