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Polynomial

FUNCTIONS If ...

Question

FUNCTIONS If f(x) is a polynomial satisfying f(x).f(y) = f(x) + f(y) + f(xy) - 2, for all x,y belong to R and f(2) = 5, then show that f(x) is an even function.

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f

2 + f (x) \cdot f (y) = f (x) + f (y) + f (x y), \forall x, y ϵ R

f (2) = 5

f (f (2))

f

f (x) f (y) = f (x) + f (y) + f (x y) - 2

x, y \in R

f (2) = 5

{lim}_{x \to 4} f (x)

Given that $f (x)$
is a differentiable function of $x$ and that $f (x)$ . $f (y)$ = $f (x)$ + $f (y)$ + $f (x y) - 2$ and that
$f (2) = 5$ .

Then $f (3)$ is equal to?

f (x)

f (x y) = f (x) + f (y)

f (2) = 1

f (x)

x, y

f

f (x) + f (y) + f (x) . f (y) = 1

f (x) > 0

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