$\mathrm{Let} f:R\to R$ be a function such that $f\left(0\right)=1$ and for any $x,y\in R,f\left(xy+1\right)=f\left(x\right)f\left(y\right)-f\left(y\right)-x+2.$ Then f is

• A

  one-one and onto

• B

  one-one but not onto

• C

  many one but onto

• D

  many one and into