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 -> B and g : B -> C be two functions and gof: A -> C is define statement(s) is true? a. If gof is one-one, then f anf g both are one-one b. if gof is one-one, then f is one-one c. If gof is a bijection, then f is one-one and g is onto d. If f and g are both one-one, then gof is one-one.

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

Let f : A rarr B and g : B rarr C be onto functions, show that gof is an onto function.

Give examples of two functions f : NrarrN and g : NrarrN such that g o f is onto but f is not onto.

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then 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

Lert f : X rarr Y be such that fof = f. Show that f is onto if and only if f is one-one.

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) , where m!=n . Then, f is one-one onto (b) f is one-one into (c) f is many one onto (d) f is many one into

Let f: X rarr Y be a function defined by f(x) = a sin ( x + pi/4 ) + b cosx + c. If f is both one-one and onto, then find the set X and Y

If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, when x is rational and x, when x is irrational then (f-g) is A. one-one and onto B. neither one-one nor onto C. many one and onto D one-one and into