Linear operator A is defined as
A(C_1f(x)+C_2g(x))=C_1Af(x)+C_2Ag(x)
Question. Is A=5 a linear operator? I know that this is just number but it satisfy relation
5(C_1f(x)+C_2g(x))=C_15f(x)+C_25g(x)
but it is also scalar.
Is function ##A=x## linear operator? It also satisfy...
I know that. But I asked only for logarithm because
\log (ab)=\log (a)+\log (b)
\log ((-a)(-b))=\log (a)+\log (b)
Why function ##f(x)=e^x## isn't surjective?
Homomorphism is defined by ##f(x*y)=f(x)\cdot f(y)##. One interesting example of this is logarithm function ##log(xy)=\log x+\log y##. Can you explain me why this is also isomorphism?