Asked by fatima
show that the composition of two increasing functions is increasing
Answers
Answered by
Steve
(fog)(x) = f(g(x))
f(x+h) > f(x) if h>0
g(x+h) > g(x) if h>0, so g(x+h) = g(x) + k for some value of k
consider f(g(x+h)). g(x+h) > g(x), so
f(g(x+h)) > f(g(x))
so, increasing
f(x+h) > f(x) if h>0
g(x+h) > g(x) if h>0, so g(x+h) = g(x) + k for some value of k
consider f(g(x+h)). g(x+h) > g(x), so
f(g(x+h)) > f(g(x))
so, increasing
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