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Question

Let g(x)>0 and f(x)<0xϵR, then

A
f(f(x+1))>f(f(x1))
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B
f(g(x1))>f(g(x+1))
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C
g(f(x+1))>g(f(x1))
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D
g(g(x+1))>g(g(x1))
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Solution

The correct options are
B f(g(x1))>f(g(x+1))
C f(f(x+1))>f(f(x1))
D g(g(x+1))>g(g(x1))
Given g(x)>0 and f(x)<0
g(x) is increasing and f(x) is decreasing.
Now option A,
Hence, f(x+1)<f(x1)
f(f(x+1))>f(f(x1))
option B,
Hence, g(x1)<g(x+1)
f(g(x1))>f(g(x+1))
option C,
Hence, f(x+1)<f(x1)
g(f(x1))>g(f(x+1))
option D,
Hence, g(x1)<g(x+1)
g(g(x+1))>g(g(x1))
Therefore option A,B,D are correct

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