# homomorphism

Take $(a,b),(c,d)\in \mathbb{R}^+ \times \mathbb{Z}_2$ then $f((a,b)(c,d))=ac(-1)^{b+d}=ac(-1)^b(-1)^d=a(-1)^bc(-1)^d=f((a,b))f((c,d))$
I'm assuming $\mathbb{R} ^+$ is the group of postitive real numbers with multiplication as operation.