Prove that the function `f: RR rarr RR ` defined by, `f(x)=sin x`, for all `x in RR` is neither one -one nor onto.

Prove that the mapping f: RR rarr RR defined by , f(x)=x^(2)+1 for all x in RR is neither one-one nor onto.

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

Let A be the set of quadrilaterals in a plane and RR^(+) be the set of positive real numbers. Prove that, the function f: A rarr RR ^(+) defined by f(x) = area of quadrilateral x, is * many-one and onto.

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

Prove that the greatest integer function f: RR rarr RR , given by f(x)=[x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Let A be the set of triangles in a plane and RR^(+) be the set of positive real numbers. Then show that, the function f:A rarr RR^(+) defined by , f(x)= area of triangle x, is many -one and onto.

Let the function f: RR rarr RR be defined by, f(x)=x^(3)-6 , for all x in RR . Show that, f is bijective. Also find a formula that defines f ^(-1) (x) .

Let CC and RR be the sets of complex numbers and real numbers respectively . Show that, the mapping f:CC rarr RR defined by, f(z)=|z| , for all z in CC is niether injective nor surjective.

Show that the modulus function f: RR rarr RR , given by f(x)=|x| is neither one-one nor onto Where |x|={(x " when "x ge 0),(-x " when " x lt 0):}

Show that , the function f: RR rarr RR defined by f(x) =x^(3)+x is bijective, here RR is the set of real numbers.