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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))= x 2 +2 then what is f(3)

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)

Grade:12th Pass

1 Answers

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

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