Let f ST, 9: TU and h : U V be functions. Composition of functions...

 

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Let f ST, 9: TU and h : U → V be functions. Composition of functions is associative. i.e. ho (go f) = (hog) of. If f and g are one-to-one, then go f is one-to-one. If ƒ and g are onto, then go f is onto. and onto. Let f ST be a function. Then ƒ has an inverse if and only if f is one-to-one Let S and T be finite sets. If ƒ : S → T is one-to-one or onto, then f is a one-to-one correspondence. Let f ST, 9: TU and h : U → V be functions. Composition of functions is associative. i.e. ho (go f) = (hog) of. If f and g are one-to-one, then go f is one-to-one. If ƒ and g are onto, then go f is onto. and onto. Let f ST be a function. Then ƒ has an inverse if and only if f is one-to-one Let S and T be finite sets. If ƒ : S → T is one-to-one or onto, then f is a one-to-one correspondence.