cool function

Number Theory Level 2

Let f : R ⟶ R f: R \longrightarrow R be a function such that f ( 0 ) = 1 f(0)=1 and for any x , y ∈ R x,y \in R that f ( x y + 1 ) = f ( x ) f ( y ) − f ( y ) − x + 2 f(xy+1)=f(x)f(y)-f(y)-x+2 . Then find f ( x ) f(x) .

x 2 + x x^{2}+x x+1 sin ⁡ x \sin x Cannot find

Indulal Gopal by indulal gopal , 49, India

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1 solution

Ramesh Goenka
Oct 27, 2014

first find the value of f(1) by replacing x and y equal to 0, then replacing y with 0 will give f(x).

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Congrats [Ramesh] (https://brilliant.org/profile/ramesh-390p9d/)

indulal gopal - 6 years, 7 months ago

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