A) \[f\{g(x)\}\ge f\{g(0)\}\]
B) \[g\{f(x)\}\le g\{f(0)\}\]
C) \[f\{g(2)\}=7\]
D) None of these
Correct Answer: B
Solution :
[b] \[f'(x)>0\] if \[x\ge 0\] and \[g'(x)<0\] if \[x\ge 0\] Let \[h(x)=f(g(x))\] then \[h'(x)=f'(g(x)).g'(x)<0\] if \[x\ge 0\] \[\therefore h(x)\] is decreasing function \[\therefore h(x)\le h(0)\] if \[x\ge 0\] \[\therefore f(g(x))\le f(g(0))=0\] But codomain of each function is \[[0,\infty )\] \[\therefore f(g(x))=0\] for all \[x\ge 0\] \[\therefore f(g(x))=0\] Also \[g(f(x))\le g(f(0))\] [as above]
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