Functions

Q: Functions f(x) and g(x) are defined in [a,b] such that f(x) is monotonically increasing while g(x) is monotonically decreasing.

If it is given that range of f(X) and g(x) are subsets of the domain, then find the domain and range of

h(x) = f(g(x))+g(f(x))

2 Answers

262

Aditya Bhutra ·2012-03-17 00:02:37

f(g(x)) and g(f(x)) both are decreasing functions.

thus f(g(b)) +g(f(b)) â‰¤ h(x) â‰¤ f(g(a)) +g(f(a))

Oh, I didn't pay attention to it. Thanks for clarifying.

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