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Show that if f: AtoB and g: Bto C are o...

Show that if f: `AtoB` and g: `Bto C` are onto,then go f : `AtoC` is also onto.

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

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

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

Show that if f: A to B and g : B to C are one-one then fog: A to C is also one-one.

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

Consider a function f: [0, (pi)/(2)] to R given by f (x) = sin x and g : [0, (pi)/(2)] to R given by g (x) = cos x, Show that f and g are one-one but f + g is not one-one.