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

Let A = R -{3} , B = R - {1} and let f: A rarr B be defined by f(x) = (x-2)/(x-3) . Check the nature of function.

If the function f :R rarr A given by f(x) = x^2/(x^2+1) is surjection , then find A.

If f: R rarr R is given by f(x) = (x^2 -4)/(x^2+1) , identify the type of function.

Let A=R-{3} and B=R-{1} consider the function f:ArarrB defined by f(x)=(x-2)/(x-3) .Is it invertible?Why?

Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-one but not onto.

Let A = R - {-3} and B = R - {1} Consider the function f : A rarr B defined by f(x) = (x-2)/(x-3) . Is f one-one and onto ? Justify your answer.

Show that the function f : R_** rarr R_** defined by f (x) = 1/x is one-one and onto,where R_** is the set of all non-zero real numbers. Is the result true, if the domain R_** is replaced by N with co-domain being same as R_** ?

Show that the function f:R rarr R given by f(x)=x^3 is injective.

Consider the function f:R rarr R defined by f(x)=|x-1| . Is f(2)=f(0) ,why?