dear sir .i have one problem to be solved.
IF F(x) is increasing in [0,infinity]and G(x)is decreasing insame interval and H(x)=F{G(x)}and H(0)=O then prove that
H(x)is constant .
Acc. to me the fn. H(x) should be decreasing as per the details given by you.(can be proved both graphically and mathematically)
make sure the question is complete.
pls. post what do you think abt this fn.
make sure the question is complete.
pls. post what do you think abt this fn.
Let us assume 2 arbitrary points a and b such that a<b. As g(x) is a decreasing function,
g(a)>g(b)
as f(x)is increasing,
f{g(a)}>f{g(b)}
i.e.h(a)>h(b)
Hence,h(x) is decreasing as a<b.
I am getting the same answer as Paritosh.Pls check if there is a mistake in your question.