A question about isomorphic between two groups

Question

For groups $G_1,G_2$ define $f:G_1\rightarrow G_2$ by $f(x)=e^x$. This bijection is an isomorphism hence (3) is correct

can any one explain for remaining i am so thank full advance

Answer 1

1. False. Look at the cardinality.

2. Suppose true and $f(x)=-1$. Then $f(x/2+x/2)=f(x/2)^2=-1$ which is impossible

3. Take $\exp$ I assume real numbers >0

4. Suppose true and $f(x)=2$. Then $f(x/2+x/2)=f(x/2)^2=2$ which is impossibe in $\mathbb{Q}$.