Functions Question 709
The range of the function $ f(x) = P_{x-3}^{7-x} $ is
Options:
A) $ {1,2,3} $
B) $ {1,2,3,4,5,6} $
C) $ {1,2,3,4} $
D) $ {1,2,3,4,5} $
Show Answer
Answer:
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} $
BETA
