A) \[f(g(x+1))>f(g(x+5))\]
B) \[f(g(x))<f(g(f(x+2))\]
C) \[g(f(x))<g(f(x+2))\]
D) \[g(f(x))>g(f(x-2))\]
Correct Answer: A
Solution :
[a] Given, \[f'(x)<0\] and \[g'(x)>0\] therefore g(x) is an increasing function and f?(x) is a decreasing function \[\therefore x+1<x+5\Rightarrow g(x+1)<g(x+5)\] \[\Rightarrow f(g(x+1))>f(g(x+5))\] Again \[x<x+1\Rightarrow g(x+1)\Rightarrow f(g(x))\] \[>f(g(x+1))\] \[x<x+2\Rightarrow f(x)>f(x+2)\Rightarrow g(f(x))\] \[>g(f(x+1))\] \[x>x-2\Rightarrow f(x)<f(x-2)\Rightarrow g(f(x))\] \[<g(f(x-2))\]You need to login to perform this action.
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