A) \[h(x)\,=0\forall x\ge 0\]
B) \[h(x)\,>0\forall x\ne 0\]
C) \[h(x)\,<0\forall x\ne 0\]
D) none of these
Correct Answer: A
Solution :
Given \[h(x)\]=\[g(f(x))\]. |
Since\[0\le g(x)<\infty \forall \,x\] |
\[\therefore \,h(x)\ge 0\forall \,x\in domain..\left( i \right)\] |
Again \[h'\left( x \right)=g'(f(x))\,\,f'\left( x) \right)\le 0\] |
\[\Rightarrow h(x)\,\]is decreasing function |
\[\therefore h\left( x \right)\le h(0)if\,x\ge 0\,\] |
\[\Rightarrow h\left( x \right)\le 0\forall x\ge 0\] |
\[\left( \because h(0)=0 \right)..\left( ii \right)\] |
\[\therefore \]From (i) and (ii) \[h(x)\,=0\forall x\in [0,\infty )\] |
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