Let `f:R rarr R` be such that `f(x)=2x`.Determine whether `f(x+y)=f(x).f(y)` holds?

Let f:R rarr R be such that f(x)=2x .Determine f(f(x).

If f(x)=(x-1)/(x+1) ,then show that f(1/x)=-f(x) .

Let f : R rarr R be defined as f(x)=2x+3 . Show that f is invertible and find f^-1 : R rarr R .

If f : R rarr R be defined by f(x)=|x| , show that fof=f

Let f:R rarr R is defined by f(x)=3x-2 and g:R rarr R is defined by g(x)=(x+2)/3 . Show that f.g=g.f .

Let f,g: R rarr R be defined respectively by f(x)=x+1,g(x)=2x-3 .Find f+g,f-g and f/g .

If f(x)=(x-1)/(x+1) ,then show that f(-1/x)=-1/f(x) .

Let f : R rarr R be defined as f(x)=x^3+2 . Show that f^-1 : R rarr R exists and hence find the formula for f^-1 .

If f : R rarr R be defined by f(x)=2x-3 and g : R rarr R be defined by g(x)= (x+3)/2 , show that fog=gof=I_R

Let A={9,10,11,12,13} and let f:A rarr N be defined by f(x)=the highest prime factor of n.Find the range of f.