A) \[\{1,\text{ }2,\text{ }3\}\]
B) \[\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6\}\]
C) \[\{1,2,3,4\}\]
D) \[\{1,\,\,2,\,\,3,\,\,4,\,\,5\}\]
Correct Answer: A
Solution :
The given function\[f(x){{=}^{7-x}}{{P}_{x-3}}\]would be defined, if (i)\[7-x>0\]\[\Rightarrow \]\[x<7\] (ii) \[x-3\ge 0\Rightarrow x\ge 3\] (iii) \[(x-3)\le (7-x)\] Hence Range of\[f(x)={{\{}^{4}}{{P}_{0}}{{,}^{3}}{{P}_{1}}{{,}^{2}}{{P}_{2}}\}\] Range of \[f(x)=\{1,3,2\}\]
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