Let `f: R->R` whre `R^+` is the set of all positive real numbers, be such that `f(x)=(log)_e xdot` Determine: `{x :f(x)=-2}`

Let f: R->R whre R^+ is the set of all positive real numbers, be such that f(x)=(log)_e xdot Determine: whether f(x y)=f(x)+f(y) holds.

Let f: R^+ -> R where R^+ is the set of all positive real numbers, be such that f(x)=(log)_e x . Determine: the image set of the domain of f

Let R be the set of all real numbers. The function f:Rrarr R defined by f(x)=x^(3)-3x^(2)+6x-5 is

Let f(x)=x/(1+x) and let g(x)=(rx)/(1-x) , Let S be the set off all real numbers r such that f(g(x))=g(f(x)) for infinitely many real number x. The number of elements in set S is

If R is the set of real numbers prove that a function f: R -> R,f(x)=e^x , x in R is one to one mapping.

Let R^+ be the set of all non-negative real numbers. If f: R^+\ ->R^+ and g: R^+\ ->R^+ are defined as f(x)=x^2 and g(x)=+sqrt(x) . Find fog and gof . Are they equal functions.

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 whose domain is the set of all real number. If f(x)=|x|-x , what is the range of f?

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) The value of f(10) is equal to