Show that the function f in `A=R-{2/3}`defined as `f(x)=(4x+3)/(6x-4)` 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_** ?

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.

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

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

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.

Let A=R-{3} and B=R-{1} Consider the function f:ArarrB 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 modulus function f: R rarr R given by f(x) = |x| , is neither one-one nor onto.

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 .Is f a one-one function?Why?