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.

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

Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| for all xdot Then 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

Show that the statement, "if f and gof are one-to-one, then g is one-to-one", is not true.

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

State whether the following relations are functions or not. If it is a function check for one- to- oneness and ontoness. If it is not a function state why? If A= {a,b,c} and f= {(a,c) (b,c) (c,b)}: (f:A to A).

State whether the following relations are functions or not. If it is a function check for one- to- oneness and ontoness. If it is not a function state why? If X = { x,y,z } and f= {(x,y) (x,z) (z,x) } : (f: X to X)

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