A) \[\{1,2,3\}\]
B) \[\{1,2,3,4,5,6\}\]
C) \[\{1,2,3,4\}\]
D) \[\{1,2,3,4,5\}\]
Correct Answer: A
Solution :
[a] 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) \[(x-3)\le (7-x)\Rightarrow 2x\le 10\Rightarrow x\le 5\] \[\Rightarrow x=3,4,5,\] 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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