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Let f : R to R be a function such that f...

Let `f : R to R` be a function such that `f(0)=1` and for any `x,y in R, f(xy+1)=f(x)f(y)-f(y)-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

Text Solution

Verified by Experts

The correct Answer is:
A
`f(xy+1)=f(yx+1)`
`f(x)f(y)-f(y)-x+2=f(y)f(x)-f(x)-y+2`
`f(x) -f(y)=x-y`
Putting `y=0`
`f(x)-1=x-0`
`f(x) = x+1`
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