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 the function f: RvecR be defined by f(x)=x+sinxforx in Rdot Then f is one-to-one and onto one-to-one but not onto onto but not-one-to-one neither one-to-one nor onto

If f:[0,oo]->[0,oo) and f(x)=x/(1+x), then f (a) one-one and onto (b)one-one but not onto (c)onto but not one-one (d)neither on-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

f(x)={(x", if x is rational"),(0", if x is irrational"):}, g(x)={(0", if x is rational"),(x", if x is irrational"):} Then, (f-g) is (A) one-one and onto (B) one-one but nor onto (C) onto but not one-one (D) neither one-one nor onto

Show that the function f:N to N defined by f(x)=2x-1 is one-one but not 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

Let f: R-> R , be defined as f(x) = e^(x^2)+ cos x , then 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.

If the function f :(-2,2]toS is defined by f(x) = x^(2) is onto then Sis: