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

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

The function f:(-oo,-1)rarr(0, e^5) defined by f(x)=e^(x^3-3x+2) is (a)many one and onto (b)many one and into (c)one-one and onto (d)one-one and into

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). f(x) is (A) one-one and onto (B) one-one and into (C) many-one and onto (D) many-one and into

Let f : R^+ ->{-1, 0, 1} defined by f(x) = sgn(x-x^4 + x^7-x^8-1) where sgn denotes signum function then f(x) is (1) many- one and onto (2) many-one and into (3) one-one and onto (4) one- one and into

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 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 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 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

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