Show that the function f : R → R, defined as f(x) = x2 , is neither one-one nor onto.

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Show that the function f : R rarr R defined by f(x) = cos (5x+3) is neither one-one not onto.

Show that the modulus function f: R->R , given by f(x)=|x| is neither one-one nor onto.

If A={x : x in R, (-pi)/(2) le x le (pi)/(2)}, B={y : y in R, -1 le y le 1} , then show that the function f: A to B defined as f(x)=sin x , x in A is one-one onto function.

Show that the function f:R->R defined by f(x)=x/(x^2+1) AA x in R is neither one-one nor onto. Also if g:R->R is defined by g(x)=2x-1 find fog(x)

Show that the function f: R_0->R_0 , defined as f(x)=1/x , is one-one onto, where R_0 is the set of all non-zero real numbers. Is the result true, if the domain R_0 is replaced by N with co-domain being same as R_0 ?

Prove that the Greatest Integer Function f : R->R , given by f (x) = [x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

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

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