For each of the following mappings
a.
c.
e.
g.
i.
k.
m.
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Elements Of Modern Algebra
- For each of the functions below, indicate whether the function is onto, one-to-one, neither or both. If the function is not onto or not one-to-one, give an example showing why. (a) f:ZxZ+Z x Z. f(1,y) = (y - 2)arrow_forwardLet ƒ(x) = x - 3, g(x) = 2x, h(x) = x3, and j(x) = 2x. Express each of the functions in Exercises 11 and 12 as a composition involving one or more of ƒ, g, h, and j.arrow_forwardLetf(x) =x2+ 4,f:R→R.(a) This function is not injective. Explain why.(b) This function is not surjective. Explain why.(c) On what domain/codomain would it be bijective? Redefine the mapping so that it is bijective.(d) Find the inverse of the function on this new domain/codomain, and specify its algebraic formand its domain/codomain mapping.arrow_forward
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