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xsw001
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f:R->R is odd, if f(-x)=-f(x) for all x
Show if f:R->R is odd and the restriction of this function to the interval [0, infinity) is strictly increasing
Then f:R->R itself is strictly increasing
I’m very confused about what the question is exactly asking for. From my understanding of the question is that I have any odd function and the graph is strictly increasing in the first quadratic . I need to prove entire graph of such odd function is strictly increasing? Am I interpreting it correctly?
I know how to prove for a strictly increasing function. Let u, v in R, find f(v)-f(u)>0, then f:R->R is strictly increasing function.
Proof:
Given f is an odd function and f is strictly increasing in [0, infinity)
Then f(D) = I, the image of the function is an interval
Therefore f is continuous and strictly increasing?
Show if f:R->R is odd and the restriction of this function to the interval [0, infinity) is strictly increasing
Then f:R->R itself is strictly increasing
I’m very confused about what the question is exactly asking for. From my understanding of the question is that I have any odd function and the graph is strictly increasing in the first quadratic . I need to prove entire graph of such odd function is strictly increasing? Am I interpreting it correctly?
I know how to prove for a strictly increasing function. Let u, v in R, find f(v)-f(u)>0, then f:R->R is strictly increasing function.
Proof:
Given f is an odd function and f is strictly increasing in [0, infinity)
Then f(D) = I, the image of the function is an interval
Therefore f is continuous and strictly increasing?
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