Show that the function `f:RtoR` defined by `f(x)=2x-3` is one-one and onto. Find `f^-1`

Prove that the function f: R rarr R given by f(x)=2 x is one-one and onto.

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 in A=R-{2/3} defined as f(x)=(4x+3)/(6x-4) is one-one and onto.Hence find f^-1

Show that the function f in A=R-{2/3} defined as f(x)=(4x+3)/(6x-4) is one-one and onto.

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:AtoB defined by f(x)=frac(x-2)(x-3) . Is f one-one and onto? Justify your answer.

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

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

A fuction f:RrarrR defined by f(x)=(2x-3)/7 . Find f^-1

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