Suppose f: A B and g: BC. Show that if f and g are one-to-one, then...

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Suppose f: A→ B and g: BC. Show that if f and g are one-to-one, then go f is one-to-one. (b) Suppose f: A → B and g: B → C. Show that if g of is one-to-one, then f is one-to-one. (c) Suppose f: A → B and g: BC. Show that if go f is onto, then g is onto. (d) Give an example of functions f: A→ B and g: BC, such that gof is onto, but f is not onto. (e) Suppose f: A → B and g: B → C. Show that if go f is onto, and g is one-to-one, then f is onto. (f) Suppose f: A → B and g: B → C. Show that if f is onto and go f is 1-1, then g is 1-1. (g) Define f: [0,00) → R by f(x) = r. Find a function g: R → R such that gof is one-to-one, but g is not one-to-one. (h) Suppose f and g are functions from A to A. If f(a): = a for every a € A, then what are fog and go f? Suppose f: A→ B and g: BC. Show that if f and g are one-to-one, then go f is one-to-one. (b) Suppose f: A → B and g: B → C. Show that if g of is one-to-one, then f is one-to-one. (c) Suppose f: A → B and g: BC. Show that if go f is onto, then g is onto. (d) Give an example of functions f: A→ B and g: BC, such that gof is onto, but f is not onto. (e) Suppose f: A → B and g: B → C. Show that if go f is onto, and g is one-to-one, then f is onto. (f) Suppose f: A → B and g: B → C. Show that if f is onto and go f is 1-1, then g is 1-1. (g) Define f: [0,00) → R by f(x) = r. Find a function g: R → R such that gof is one-to-one, but g is not one-to-one. (h) Suppose f and g are functions from A to A. If f(a): = a for every a € A, then what are fog and go f?

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b To show that if gof is onetoone then f is onetoone we can prove the contrapositive If f is not one... View the full answer