Show that `f: RvecR` defined by `f(x)=(x-1)(x-2)(x-3)` is surjective but not injective.

f:RrarrR" defined by "f(x)=(1)/(2)x|x|+cos+1 is

Let A={x:xepsilonR-{1}}f is defined from ArarrR as f(x)=(2x)/(x-1) then f(x) is (a) Surjective but nor injective (b) injective but nor surjective (c) neither injective surjective (d) injective

If f:RtoR is defined by f(x) = 2x - 3:

Show that the function f:N to N defined by f(x)=2x-1 is one-one but not onto.

If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, then find Adot

Let A=R-{3},B=R-{1}, and let f: AvecB be defined by f(x)=(x-2)/(x-3) is f invertible? Explain.

Let f:[-oo,0)->(1,oo) be defined as f(x)=(1+sqrt(-x))-(sqrt(-x)-x) then f(x) is (A) injective but not surjective (B) injective as well as surjective (C) neither injective nor surjective (D) surjective nut not injective

Let R be the set of real numbers. If f:R->R is a function defined by f(x)=x^2, then f is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) none of these

Show that the function defined by f(x)= cos (x^2) is a continuous function.

Show that the function defined by f(x)= sin (x^2) is a continuous function.