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

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

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 .

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 :IR rarrIR is defined by f(x)=x^2-3x+2 , find f(f(x))?

If f(x)=x^(x) , then find f'(x) .

If f(x)=x|x| , then find f'(0).

Prove that f : R rarr R, f(x)=4x-5 is invertible and find f^-1(x) .

Let f : R rarr R and g : R rarr R be defined by f(x)=x^2+3x+1 and g(x)=4x-3 . Find formulas defining the compositions fog,gof,fof and gog.

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.