If `f:[0,oo)->[0,oo) and f(x)=x/(1+x),` then `f(x) is ` (a) one-one and onto (b)one-one but not onto (c)onto but not one-one (d)neither on-one nor onto

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one-to-one nor onto

Let f: RrarrRa n dg: RrarrR be two one-one and onto function such that they are the mirror images of each other about the line y=a . If h(x)=f(x)+g(x),t h e nh(x) is (a)one-one and onto (b)only one-one and not onto (c)only onto but not one-one (d)neither one-one nor onto

The function f:[0,3]->[1,29] , defined by f(x)=2x^3−15x^2+36x+1 , is (a) one-one and onto (b) onto but not one-one (c) one-one but not onto (d) neither one-one nor onto

Let A be a non- empty set of real numbers and f:A->A be such that f(f(x))=x AA x in R then f(x) is (A) bijection (B) one-one but not onto (C) onto but not one-one (D) neither one-one nor onto

A function f from the set of natural numbers to the set of integers defined by f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d; -n/2,\ w h e n\ n\ i s\ e v e n (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

f: NrarrN, where f(x)=x-(-1)^x . Then f is: (a)one-one and into (b)many-one and into (c)one-one and onto (d)many-one and onto

For real x, let f(x)""=""x^3+""5x""+""1 , then (1) f is oneone but not onto R (2) f is onto R but not oneone (3) f is oneone and onto R (4) f is neither oneone nor onto R

If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)={(0, x in rational) (x ,x in irrational) and g(x)={(O, x in irrational x), (x in rational) then (f-g)(x)i s (a)one-one and onto (b)neither one-one nor onto (c)one-one but not onto (d)onto but not one-one

Let f: R-> R , be defined as f(x) = e^(x^2)+ cos x , then f is (a) one-one and onto (b) one-one and into (c) many-one and onto (d) many-one and into

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