For all real numbers x, let `f(x) =1/(2011sqrt(1-x^2011).`Evaluate `(f(f...f (2011)))^2011` ,where fis applied 2010 times2010 times

For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Find the number of real roots of the equation f(f (.....(f(x)).....)= ({-x} where f is applies 2013 times and {.} denotes fractional part function.

For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Find the number of real roots of the equation f(f (.....(f(x)).....)= ({-x} where f is applies 2013 times and {.} denotes fractional part function.

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___

Let f be a function defined on R (the set of all real numbers) such that f'(x)=2010(x-2009)(x-2010)^(2)(x-2011)^(3)(x-2012)^(4) for all x in R. If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___

For all real numbers x, let the mapping f (x) = 1/(x-i) . where i =sqrt -1 . If there exist real number a, b, c and d for which f(a), f(b), f(c) and f(d) form a square on the complex plane. Find the area of the square.

For all real numbers x,let the mapping f(x)=(1)/(x-i) .where i=sqrt(-1) .If there exist real number a,b,c and d for which f(a),f(b),f(c) and f(d) form a square on the complex plane.Find the area of the square.