Let `g(x)=x^(2)-4x-5` then g(x) is
(A) is one-one on R (B) g is one - one on `(-oo,2]` (C) g is not one-one on `(-oo,4]` (D) g is one - one on `(-oo,0)`

f: R rarr R,f(x)=x|x| is (A) one-one but not onto (B) onto but not one-one (C) Both one-one and onto (D) neither one-one nor onto

If fandg are one-one functions,then (a) f+g is one one (b) fg is one one one (c)fog is one one (d) noneofthese

Let N be the set of numbers and two functions f and g be defined as f,g:N to N such that f(n)={((n+1)/(2), ,"if n is odd"),((n)/(2),,"if n is even"):} and g(n)=n-(-1)^(n) . Then, fog is (A) one-one but not onto (B) onto but not one-one (C) both one-one and onto (D) neither one-one nor onto

If f(x) = x^3 + 3x^2 + 12x - 2 sin x, where f: R rarr R, then (A) f(x) is many-one and onto (B) f(x) is one-one and onto(C) f(x) is one-one and into (D) f(x) is many-one and into

Let f: R->R be a function defined by f(x)=(x^2-8)/(x^2+2) . Then, f is (a) one-one but not onto (b) one-one and onto (c) 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

if f(g(x)) is one-one function,then (1)g(x) must be one- one (2) f(x) must be one- one (3)f(x) may not be one-one (4)g(x) may not be one-one

If f:NrarrN is given by f(x)={((x+1)/(2), if x " is odd"),((x)/(2),if x " is even"):} and g:NrarrN is given by g(x)=x-(-1)^x, then f(g(x)) is (a) one one and onto (b) may one and onto (c) one one and not onto (d) neither one-one onto

Which of the following statements are incorrect? If f(x) and g(x) are one-one then f(x)+g(x) is also one-one If f(x) and g(x) are one-one then f(x)dotg(x) is also one-one If f(x) is odd then it is necessarily one-one? Ia n dI Ion l y b. I Ia n dI I Ion l y c. I I Ia n dIon l y d. I ,I Ia n dI I I

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