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# If x,f(x),a,b are positive integers, if a>b then f(a)>f(b). Now if f(f(x))= x2+2 then what is f(3)

Param
25 Points
2 years ago
$\large f(f(x)) = x^{2}+2$
f(x) will be the inverse of the above function.
now we must assume the other function in order to find the inverse of it.

$\large f(x) = f^{-1}(x^{2}+2)$
$\large Y = x^{2}+2$
$\large x = \sqrt{Y-2}$
replacing Y by x and x by Y
$\large f(x) =\pm \sqrt{x-2}$
$\large f(3) = 1 or f(3) = -1$
Since f(3) is +ve integer,
$\large f(3) = 1$