The mapping `f: R->R` given by `f(x) = x^3 + ax^2 + bx + c` is bijection if

The values of a and b for which the map f: R to R , given by f(x)=ax+b (a,b in R) is a bijection with fof as indentity function, are

The values of a and b for which the map f: R to R , given by f(x)=ax+b (a,b in R) is a bijection with fof as indentity function, are

Show that the function f: R->R given by f(x)=x^3+x is a bijection.

Show that the function f: R->R defined by f(x)=3x^3+5 for all x in R is a bijection.

Show that the function f: RrarrR given by f(x)= ax + b where a, b in R, ane0 is a bijection.

Show that the logarithmic function f: R0+->R given by f(x)=(log)_a x ,\ a >0 is a bijection.

Prove that the function f : R to R defined by f(x) = 3 - 4x , AA x in R is bijective.

Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is bijection.

Show that the function f: Rvec R given by f(x)=x^3+x is a bijection.

Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(x)=x|x| is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) none of these