Let `f(x)=2x-sinxa n dg(x)=x3` . Then A. range of `gof` is `R` B. `gof` is one-one C. both `f` and `g` are one-one D. both `f` and `g` are onto

Let f(x)=sin x and g(x)=In|x|. If the ranges of the composition functions fog and gof are R_(1), and R_(2) respectively,then

Consider functions f and g such that composite gof is defined and is one-one.Are f and g both necessarily one-one.

Let f:Nrarr R,f(x)=2x-1 g:z rarrR,g(x)=(x^(2))/(2) , then (gof)(0) is :

Prove that f:R rarr R, given by f(x)=2x, is one-one and onto.

Let f:A rarr B and g:B rarr C be two functions.Then; if gof is onto then g is onto; if gof is one one then f is one-one and if gof is onto and g is one one then f is onto and if gof is one one and f is onto then g is one one.

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

Let the function f:R rarr R be defined by f(x)=2x+sin x for x in R .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 N be the set of natural numbers and f : N->N be a function given by f(x)=x+1 for x in N.Which one of the following is correct? a. f is one-one and onto b. f is one-one but not onto c. f is only onto d. f is neither one-one nor onto

If a function f:[2,\ oo)->R defined by f(x)=(x-1)(x-2)(x-3) is (a) one-one but not onto (b) onto but not one-one (c) both one and onto (d) neither one-one nor onto