Defined as ( mn )˘ mn 2 and g(m,n)˘(m¯1,m¯n)Findtheformulasforg– f and f –g Note g– f ( m,n )˘)) mn 2¯1 Thus g– f ( m,n )˘ mn¯1 2 Note f– g (m,nWe must show that if f(n) and g(n) are monotonically increasing functions, then so is f(n) g(n) Suppose not Let n1 f(n2)g(n2) Now, f(n1) ≤ f(n2) and g(n1) ≤ g(n2) f(n1) ≤ f(n2) f(n1)g(n1) ≤ f(n2) g(n1) f(n1)g(n1) ≤ f(n2) g(n2) This contradicts our assumption (b) We must show that if f(n) and g(n) areCalled the inverse of f if g(f(s)) = s for all s ∈ S and f (g(t)) = t for all t ∈ T I proved the following result earlier Theorem Let S and T be sets, and let f S → T be a function f is invertible if and only if f is bijective Example Let S = {a,b,c,d} and T = {1,2,3,Calvin} Define f S → T by f(a) = 1, f(b) = 2, f(c) = 3, f Basic Fibroblast Growth Factor An Overview Sciencedirect Topics C-d-e-f-g-a-h-c adalah tangga nada