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 y=f(x) is one-one onto function, then: (f^-1@f)(x)=

If y=f(x) is one-one onto function, then: (fof^-1)(y)=

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

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

Statement-1 : If f(x) and g(x) are one-one functions then f(g(x)) and g(f(x)) is also a one-one function. and Statement-2 The composite function of two one-one function may or many not be one-one.

If f(x) is a one to one function, where f(x)=x^(2)-x+1 , then find the inverse of the f(x):

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 be a one-one function satisfying f'(x)=f(x) then (f^(-1))''(x) is equal to

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