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Let f: A to B and g: B to C be two funct...

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.

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Let `z in D,` then there is some `y in C` such that `g(y)=z`
` :.` Now if `y notin B`, then there is no x for which `f(x)=y`
` :. gof` is not onto.
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