Show that , the function `f: RR rarr RR` defined by `f(x) =x^(3)+x` is bijective, here `RR` is the set of real numbers.

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

The function f : RR to RR is defined by f(x) = sin x + cos x is

Let the function f:RR rarr RR be defined by f(x)=x^(2) (RR being the set of real numbers), then f is __

Find the image set of the domain of each of the following functions : g:RR to RR defined by, g(x) = x^2+2, for all x in RR, where RR is the set of real numbers.

The largest domain on which the function f: RR rarr RR defined by f(x)=x^(2) is ___

Discuss the bijectivity of the following mapping : f: RR rarr RR defined by f (x) = ax^(3) +b,x in RR and a ne 0' RR being the set of real numbers

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

If RR rarrC is defined by f(x)=e^(2ix)" for x in RR then, f is (where C denotes the set of all complex numbers)

Let the function f:RR rarr RR be defined by , f(x)=3x-2 and g(x)=3x-2 (RR being the set of real numbers), then (f o g)(x)=

Let A=RR-{2} and B=RR-{1} . Show that, the function f:A rarr B defined by f(x)=(x-3)/(x-2) is bijective .