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46 Bijections and Inverse Functions A function f A → B is bijective (or f is a bijection) if each b ∈ B has exactly one preimage Since "at least one'' "at most one'' = "exactly one'', f is a bijection if and only if it is both an injection and a surjection A bijection is also called a onetoone correspondenceRestriction of a convex function to a line f Rn → R is convex if and only if the function g R → R, g(t) = f(xtv), domg = {t xtv ∈ domf} is convex (in t) for any x ∈ domf, v ∈ Rn can check convexity of f by checking convexity of functions of one variableDefinition 13 A bounded function f a,b → Ris Riemann integrable on a,b if its upper integral U(f) and lower integral L(f) are equal In that case, the Riemann integral of f on a,b, denoted by Zb a f(x)dx, Zb a f, Z a,b f or similar notations, is the common value of U(f) and L(f) An unbounded function is not Riemann integrable Math Arizona Edu ƒtƒFƒX "¯Œ^ ƒ~ƒfƒBƒAƒ€

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