Are f and g both necessarily onto, if gof is onto?

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: A to B and g: B to 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.

Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| for all xdot Then g is a. Onto if f is onto b. One-one if f is one-one c. Continuous if f is continuous d. None of these

Let f : R to R be any function and g(x) =(1) /( f (x) ) then which of the following is / are not true ? (a) g is onto of f is onto (b) g is one - one if f is onto (c) g is continuous if is continuous (d) g is differentiable if f is differentiable

Let f:AtoB . Find f(A), i.e, the range of f, if f is an onto function.

Show that if f : A ->B and g : B ->C are onto, then gof : A ->C is also onto.

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then (a) f is one-one but not onto (b) f is onto but not one-one (c) f is both one-one and onto (d) none of these

For real x, let f(x)""=""x^3+""5x""+""1 , then (1) f is oneone but not onto R (2) f is onto R but not oneone (3) f is oneone and onto R (4) f is neither oneone nor onto R

Let A be a finite set. If f: AvecA is an onto function, show that f is one-one also.

Let f:R rarr B , be a function defined f(x)=tan^(-1).(2x)/(sqrt3(1+x^(2))) , then f is both one - one and onto when B, is the interval