If `f: X rarr[1,oo)` is a function defined as `f(x)=1+3x^3,` find the superset of all the sets `X` such that `f(x)` is one-one.

If f:[1, oo) rarr [2, oo) is defined by f(x)=x+1/x , find f^(-1)(x)

If f : R to R be a function defined by f (x) = max {x,x^(3)}, find the set of all points where f (x) is not differentiable.

If f:[1, oo) rarr [1, oo) is defined as f(x) = 3^(x(x-2)) then f^(-1)(x) is equal to

If a function f: R to R is defined as f(x)=x^(3)+1 , then prove that f is one-one onto.

If f:[a,oo)rarr[a,oo) be a function defined by f(x)=x^(2)-2ax+a(a+1). If one of the solution of the equation f(x)=f^(-1)x is 2012, then the other may be

If f:[1,oo)rarr[1,oo) is defined as f(x)=3^(x(x-2)) then f^(-1)(x) is equal to

Let f : R rarr R be a function defined by f(x) = max {x,x^(3)} . The set of all points where f(x) is not differentiable is

Let f:RR rarr RR be the function defined by f(x)=x+1 . Find the function g:RR rarr RR , such that (g o f)(x)=x^(2)+3x+3

Show that function defined by f: N rarr N , f (x) = x^3 is one-one but not onto.

If f[1, oo)rarr[1, oo) is defined by f(x)=2^(x(x-1)) then f^(-1)(x)=