A) \[11.{{e}^{33}}\]
B) 33
C) 11
D) log 33
E) none of these
Correct Answer: B
Solution :
\[f(3)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(3+h)-f(3)}{h}\] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(3)f(h)-f(3)}{h}\] \[(\because f(x+y)=f(x)f(y))\] Now, \[f(x+0)=f(x)f(0)\] \[\Rightarrow \] \[f(x)[f(0)-1]=0\] Either\[f(x)=0\]or\[f(0)=1\] \[\therefore \] \[f(3)=f(3)\underset{h\to 0}{\mathop{\lim }}\,\frac{F(h)-f(0)}{h}\] \[=f(3)f(0)=f(3).11\] \[=3\times 11=33\]
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