If f'(x)>0 and g'(x)<0,x∈R then
f(g(x))>f(g(x+1))
f(g(x)<f(g(x+1))
g(f(x))⪈g(f(x+1))
g(f(x))>g(f(x–1))
Explanation for the correct option:
Finding the value.
Let f(x)=ax
g(x)=−bx, where a,b>0
Now,
f(g(x))=−abx ….(1)
f(g(x+1))=a(−b−bx)
=−abx−ab .... (2)
compare equation (1) and (2) , we get
Hence, Option ‘A’ is Correct.