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

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

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.

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 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

Show f:R rarr R defined by f(x)= x^2 + x for all x in R is many one.

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

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

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

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